In this paper, we present a state observer for single-input/single-output nonlinear systems which fail to have well defined relative degree. It is shown that there exists a local state observer for a nonlinear system if it has robust relative degree rr. The proposed observer utilizes the coordinate change which transforms a system into an approximate normal form. The proposed method is applied to a ball and beam system, and simulation results show that substantial improvement in the performance was achieved compared with other local observers.