Type III restriction/modification enzyme recognize short, non-palindromic sequences that can be methylated on only one strand, with the paradoxical consequence that during replication of what is in effect hemimethylated DNA totally unmodified sites arise. Why the unmodified sites are not subject to suicidal restriction was not clear. Here we show that restriction requires two unmodified recognition sites that can be separated by different distances but which must be in inverse orientation. All of the unmodified sites in newly replicated DNA are of course in the same orientation, which explains why they are not restricted. This result may be of relevance to other manifestations of anisotropy in double-stranded DNA, such as genetic imprinting.