The time-dependent quantum theory of molecular photodissociation of Heller is reformulated in the framework of polynomial propagation. The new formulation retains the essential features of the time-dependent approach, but requires neither propagation in time nor interpolation of the evolution operator. In this new approach, the propagation is carried out by recursion of the corresponding orthogonal polynomial, which requires minimal storage. The wave packet can be restricted to real space, further reducing cpu and memory requirements. If the wave packet is propagated by the Chebyshev operator, the total cross section can be obtained via the cosine Fourier transform from the order-dependent autocorrelation function. Like the time-dependent approach, the internal state distributions of the fragment can be projected out from the asymptotic wave packet. The nonadiabatic photodissociation of methyl iodide with two active dimensions is employed to illustrate the applicability of the new approach.