The invention essentially concerns a method for fast starting on an up slope or with a high load. Said method uses a power transmission device (1.1) comprising a traction chain. Said traction chain consists in particular of a heat engine (2), a clutch (3), an electrical macine (4), and wheels (6). The invention is characterized in that while the vehicle is stopped or is running at low speed up a slope, the heat engine (2) is stopped, and when the vehicle is accelerated, the heat engine (2) is started using a starting system (7) mechanically independent of the electrical machine.