It has been suggested that the mammalian memory system has both familiarity and recollection components. Recently, a high-capacity network to store familiarity has been proposed. Here we derive analytically the optimal learning rule for such a familiarity memory using a signal- to-noise ratio analysis. We find that in the limit of large networks the covariance rule, known to be the optimal local, linear learning rule for pattern association, is also the optimal learning rule for familiarity discrimination. In the limit of large networks, the capacity is independent of the sparseness of the patterns and the corresponding information capacity is 0.057 bits per synapse, which is somewhat less than typically found for associative networks.