A new method for the calculation of partial cross sections in the time-dependent quantum theory of molecular reactive scattering processes is discussed. Preliminary calculations are presented which clearly illustrate the power of the method. They show how all the partial cross sections associated with a single initial quantum state may be computed over a very wide energy range from a single propagation of a prepared wavepacket. The resonance behaviour is obtained without difficulty and the energies of the reactive scattering resonances are exactly reproduced.