The fact that the veteran Dane is wearing the yellow jersey on the Tour de France is not really a surprise as he did so briefly last year.
But the difference between then and now is that this time he is saying that he wants to bring it back to the Champs Elysees, where the race ends on July 21. ``My goal is to win the race and I know it will be tough but it's possible,'' said Riis, who used a shortened stage on Monday to win the coveted shirt and then kept it on Tuesday.
Before the race started, Riis was often omitted from the lists of men capable of winning the Tour. The 32-year-old rider from Herning is a long way from being an archetypal star.
But fifth place in the 1993 Tour and his third place last year clearly indicated that he was capable of matching the best in the demanding event. ``In 1993, when I finished fifth, I realised that I could do something in this race,'' said Riis, who had to wait until this season to be his team's leader.
He had earlier concentrated on helping twice winner Laurent Fignon of France in the Super-U and Castorama stables before joining Ariostea and Gewiss.
His tense relationship with Gewis leader Evgeny Berzin of Russia last year led him to move to the German stable, Telekom.
``I respect Berzin as a rider but I wouldn't say he's my friend,'' he said without elaborating.
The athletic Dane, who stands 1.84 metres tall and weighs in at 71 kilograms, has long been regarded as a strong rider, powerful in time-trials and at ease in high climbs.
But today, for the first time, he looks like a potential Tour winner.
``Since this winter Bjarne has kept telling me that he wanted to win the Tour,'' said Telekom team director Walter Godefroot.
If Riis is not as well known as Spaniard Miguel Indurain or Swiss Tony Rominger, he has enthusiastic followers who can be seen lining the roads of the Tour waving red and white Danish flags.
``I see them every day and it helps me a lot,'' he said. ``I think my little country is proud of me and that makes me happy.''
He could be even happier in a few days.
``Some years back it would have been impossible for me to think I could win a race like the Tour,'' he said. ``I just tried to help my leader the best I could.
``Now it's different. I'm not taking anything for granted but I think I can make it.''
Only the greatest cyclists of their generation have won it, and you can be sure that while some riders forsake either the Tour of Italy or the Tour of Spain none would dare miss the Tour de France.
Like any great event, its history is littered with heartbreak, memorable moments and tragedy.
If you talk of heartbreak then Laurent Fignon of France would come close to the top of those who have experienced it -- and worst of all in the almost Colosseum-like atmosphere of the Champs Elysee.
Fignon, not best loved by his home crowd -- despite being a dual winner -- after he mocked France's five-time winner Bernard Hinault in 1984, led American Greg Lemond by 58 seconds going in to the final day's time trial.
Lemond then rode one of the greatest time-trials ever and beat a floundering Fignon by eight seconds in the closest finish in the great race's history.
A memorable day for Lemond -- a disaster for Fignon, and perhaps a wry smile from Hinault.
Ireland's Stephen Roche, only the second cyclist to win the tours of Italy, France and the world championship in the same year, produced one of the most memorable and brave stage performances in 1987.
Entering the Alpine stages second overall, he trailed the Spaniard Pedro Delgado by a huge margin on the climb up to Villard de Llans.
With an almost superhuman effort, Roche counter-attacked on his own and reduced the gap to four seconds by the finish. He took over the yellow jersey, although he spent the night in hospital for his consummate bravery.
Tragedy has struck, in the real sense of the word, three times in the Tour's history. Spaniard Francisco Cepeda died in 1935 from a broken skull suffered in a fall down a ravine.
Tommy Simpson, the first Englishman to wear the overall leader's yellow jersey, collapsed and died on Mont Ventoux in the 1967 Tour.
Simpson's autopsy revealed a large amount of stimulants in his system, and led directly to the banning of many of them from cycling. Simpson had almost met with similar disaster in the 1965 Tour when a horrific fall had led to doctors debating whether to remove his arm or not.
Last year, Italian Olympic Champion Fabio Casartelli, who had found life in the professional ranks difficult, was killed when he hit his head against a stone block during a mass pile up on the descent from Portet Aspet.
His death, though, highlighted the respect and good sportsmanship that have forever been part of the peloton. During the next stage all the remaining riders rode together and at the end parted like the Red Sea to let Casartelli's Motorola teammates ride to the finish together.
Aside from these moments of great emotion, there have been the four giants who have won 20 Tours between them, and one threatens to erase all the records by winning his sixth this year.
With respect to Frenchman Louison Bobet, who won three in a row from 1953, the names of Frencman Jacques Anquetil ('57 and '61-64), Eddie Mercx of Belgium ('69-72 and '74), France's Bernard Hinault (78-79, 81-82 and 85) and Spaniard Miguel Indurain (91-95) will always dominate Tour lore.
Mercx appeared to have been able to perform Herculean tasks year in year out but it is virtually impossible to assess who ranks second to him.
Anquetil and Indurain are relatively similar, in that both were great time-triallists, strong enough climbers and were impossible to break. Also, they both never won the world road race championship, something that caused Anquetil great heartbreak, although Indurain, of course, can still accomplish that.
Hinault, known as the 'Badger', was weak in all out sprints but had the benefit of a very strong team, something which Indurain has generally lacked. Like Mercx, he finished runner-up in his final attempt to win a sixth Tour, although he was wearing the yellow jersey when he was forced to retire in the 1980 Tour.
Mercx has the edge on them all. He enjoyed 35 stage victories, seven more than Hinault, spent a record 96 days wearing the yellow jersey and in 1969 he pulled off the unique achievement of winning all three major Tour de France titles.
Not only did he win the yellow jersey but also the green jersey for points winner and the polka dot jersey for King of the Mountains. He was strong in the mountains, in time-trials and in sprints -- simply a flawless champion.
Unlike Indurain and Anquetil, he sought to break his rivals by leading from the front and as the results show he achieved it in devastating fashion.
It is little wonder, therefore, that with athletes like these dominating the sport, and with several others capturing day-to-day headlines with stirring exploits, that the Tour de France has become a target for so many countries bidding to host stages.
They, too, want to enjoy some of its dramatic and romantic allure.