We investigate a discrimination scheme between unitary processes. By introducing a margin for the probability of erroneous guess, this scheme interpolates the two standard discrimination schemes: minimum-error and unambiguous discrimination. We present solutions for two cases. One is the case of two unitary processes with general prior probabilities. The other is the case with a group symmetry: the processes comprise a projective representation of a finite group. In the latter case, we found that unambiguous discrimination is a kind of "all or nothing": the maximum success probability is either 0 or 1. We also closely analyze how entanglement with an auxiliary system improves discrimination performance.