Minardi unveiled their first new car for three years at Imola on Friday.
Minardi hope to overhaul Jordan with their new car
The new car enables Minardi to run up-to-date Cosworth engines and team boss Paul Stoddart hopes the PS05 can overhaul rival minnows Jordan.
"The PS05 looks very promising indeed in terms of our quest for ninth in the constructors' championship," he said.
"The true potential of the new car, however, will be revealed in the coming races, as the engineers and technicians come fully to understand the machine."
The Cosworth engine has powered Red Bull to 12 points so far this season.
It is the first time in several seasons that Stoddart's team have enjoyed a parity of engine supply.
But that will not last long as Cosworth are planning an engine upgrade that will only be available to Red Bull.
Cosworth managing director, Tim Routsis, said: "An upgraded engine is scheduled for introduction with Red Bull Racing at the Indianapolis Grand Prix or the Canadian Grand Prix, depending on when the scheduled engine change occurs.
"It will be exclusive to Red Bull Racing and a development version with a gain of 30bhp has already been successfully track-tested by the team."
But Stoddart remains upbeat about the immediate future, adding that Friday's unveiling marked "the true start of our 2005 season".
Minardi had a controversial start to the campaign - attempting to race in the opening Grand Prix in Australia with last year's cars, which did not conform to new aerodynamics regulations.
Stoddart fought a legal battle to win the right to race, and after securing a temporary injunction to compete in practice and Saturday's qualifying in Melbourne, he dropped the action.
Minardi mechanics hastily converted the 2004 cars to comply with the new rules, to the approval of the race officials.