  The pair contact process (PCP) is a nonequilibrium stochastic model which,
like the basic contact process (CP), exhibits a phase transition to an
absorbing state. The two models belong to the directed percolation (DP)
universality class, despite the fact that the PCP possesses infinitely many
absorbing configurations whereas the CP has but one. The critical behavior of
the PCP with hopping by particles (PCPD) is as yet unclear. Here we study a
version of the PCP in which nearest-neighbor particle {\it pairs} can hop but
individual particles cannot. Using quasistationary simulations for three values
of the diffusion probability ($D=0.1$, 0.5 and 0.9), we find convincing
evidence of DP-like critical behavior.
