In this work, the contact process (CP) is modified in order to model a contact replication process (CRP) for monoclonal reproduction. The occupation rates of an empty site depend on the nearest-neighbor and next-nearest-neighbor sites. The CRP exhibits an absorbing state transition studied through cluster approximations and Monte Carlo simulations. The critical rate obtained from simulations, lambda(c) =2.0263 (4) , is smaller than that for CP. However, the CRP critical exponents are in agreement with those for CP and, consequently, the model belongs to the directed percolation universality class.