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Nonreciprocal optical systems have found many applications altering the linear transmission of light as a function of its propagation direction. Here we consider a new class of nonreciprocity which appears in photon pair correlations and not in linear transmission. We experimentally demonstrate and theoretically verify this nonreciprocity in the second-order coherence functions of photon pairs produced by spontaneous four-wave mixing in a silicon microdisk. Reversal of the pump propagation direction can result in substantial extinction of the coherence functions without altering pump transmission.