Jenson Button believes BAR's new car will be good enough to give the top three teams a run for their money.
Button and new team-mate Takuma Sato have been testing a development version of the 2004 BAR in Spain.
And the British driver is confident it will allow BAR to trouble Ferrari, Williams and McLaren.
"We've seen improvements in areas we've not even been working on. Compared to last year, it's a big step forward," he told this website.
"We expect to be fighting with the top three teams. We wouldn't be saying it if we didn't expect it.
"I don't think that we have a chance of winning the title, but I think we can be challenging McLaren, Ferrari and Williams - and not just on occasions."
BAR ended up fifth in the constructors' standings last season - with Button claiming 17 of their 26 points - after an impressive final race in Japan.
But they were dogged by reliability problems, finishing 62 points behind fourth-placed Renault - with a further yawning gap to McLaren, Williams and champions Ferrari.
"I think a lot of people are going to be impressed with our step forward," said Button. "Fourth in the championship would be great for us, but we want to be third or better.
"We want to be consistent, we want to be reliable and be on the podium as much as possible. Everyone wants to be, but I think we do have the possibility."
Button has taken time out from testing to shoot an advertisement campaign for the BBCi on TV service, which gives the BBC's digital viewers access to the latest news, sport and entertainment information.
He has already done five days in BAR's interim car - now running on Michelin rather than Bridgestone tyres - with Sato at Barcelona and Jerez.
And Button said the early signs from Honda's new engine, which is smaller and lighter than last season's, were good.
"Sometimes this year we did struggle with reliability," admitted Button. "We were probably one of the weakest teams in that area.
"We've been working on that a lot with the interim car, which has a new rear end, engine, gearbox and suspension, and it's run perfectly.
"We've done five days' testing and not had one problem. It's more reliable than the old car already.
"With the new regulations next season, you will only be able to use one engine for the whole race weekend, so the engine will have to do twice the distance.
"It's very unusual for a brand new F1 car to be so reliable, so now we've got that we can work on other areas."