The farewell model, a Grand Sport Vitesse, takes its exterior design cues from the very first Veyron -- chassis #01 -- and the two cars were unveiled side by side at the Geneva Motor Show on Tuesday.

However, while the very first customer Veyron was finished in black and red paint, the 450th example is finished in exposed red- or black-tinted carbon fiber, a technique the marque has pioneered over the past decade.

There are two other big differences: The 450th Veyron is a convertible rather than a hard top and its engine more potent. Bugatti's engineers wanted to ensure that it could retain its crown as the world's fastest production car.

Every Bugatti that leaves the factory does so with its prospective owner's input and La Finale is no exception. The owner -- the car has already been sold -- has gone for subtlety. The only clues as to the car's significance are a small "La Finale" badge under the right headlamp and the same legend written on the underside of the car's airbrake spoiler; meaning it is only visible when the car is braking sharply.

When Ferdinand Piech, the head of Bugatti's parent company, Volkswagen, said that he wanted the company to build a car with 1000bhp, a top speed in excess of 400km/h (250mph) and a 0-100km/h time of less than 3 seconds, but still be suitable for driving to the opera in comfort and style even his engineers were skeptical.

However, over the past decade, the resulting car has become a symbol of what is possible without breaking the laws of physics.

It debuted with an 8-litre, quad-turbo W16 engine, 987bhp (1001PS) and top speed of 252.97mph (407.12km/h) and a 0-100km/h time of just under 2.5 seconds, making it the fastest and most powerful production car in history. Before the Veyron arrived, there wasn't a gearbox capable of channeling that much power, nor where there road legal tires capable of handling those statistics.

When other companies started to catch up to the Veyron, Bugatti turned up the power even more with the Supersport which outputs 1184bhp, is capable of going from 0-100km/h in just 2.2 seconds and onto a top speed of 268mph (431km/h).

And now that the car's production run is ended, Bugatti will be working on a replacement model which it hopes to debut next year and which promises to carry on where the old car left off.