This paper presents a control design for the tip position trajectory tracking of a two-link manipulator arm with a flexible forearm. The control design is based on two steps. First, input-output linearization is applied to decouple the shoulder arm dynamics from the forearm dynamics, which transforms the trajectory tracking control of the nonlinear non-minimum phase system into the trajectory tracking control of two linear subsystems. Then trajectory tracking control design of each subsystem is carried out in the second design step. Stability and performance properties of the control design are presented together with simulation results. This study demonstrates a control design method for trajectory tracking control of a nonlinear non-minimum phase system.