A variational principle, which has as its stationary conditions the direct and adjoint time-dependent group diffusion equations, is modified to admit time-discontinuous approximating functions. This extended principle is used to develop a synthesis approximation for the time-dependent group diffusion equations which permits the use of different sets of trial functions at different times during a transient analysis. The necessary equations are derived in detail, and two numerical examples are presented. These examples show that the time-discontinuous synthesis method is capable of constructing accurate space-time neutron fluxes, which vary smoothly in time, from spatial trial functions which are discontinuous in time. In addition, these examples display the potential of the new time synthesis for yielding computationally less expensive solutions than are possible with the time-continuous synthesis procedure.