The problem of designing a parallel feedforward compensator (PFC) is considered for a class of non-square linear systems such that the closed-loop system is strictly passive. If a given square system has (vector) relative degree one and is weakly minimum phase, the system can be rendered passive by a state feedback. However, when the system states are not always measurable and the given output is considered, passivation (i.e. rendering passive) of a non-minimum phase system or a system with high relative degree cannot be achieved by any other methodologies except by using a PFC. To passivate a non-square system we first determine a squaring gain matrix and design a PFC such that the composite system has relative degree one and is minimum phase. Then the system is rendered strictly passvie by a static output feedback law. Necessary and sufficient conditions for the existence of the PFC and the squaring gain matrix are given by the static output feedback formulation, which enables to utilize linear matrix inequality (LMI). As an application of the scheme, an alternative way of replacing the role of velocity measurements is provided for the PD-control law of a convey-crane system.