Summary: The problem of finite/infinite transmission zero assignment is examined by squaring a system from the outputs to the inputs. In particular, we study this problem in two cases, state-accessible systems and partially state-accessible systems. We show that the problem of transmission zero assignment for state-accessible state-variable systems is equivalent to a pole-placement problem with state feedback for a generalized system, which always has a solution. In the case of partially state-accessible systems, we show that the transmission zero assignment problem is equivalent to a pole-placement problem with output feedback for a generalized system. In both cases we exploit the block Hessenberg form of the system and the extended lower triangular Hessenberg form in order to formulate this problem.