This paper deals with the problem to estimate some states of a multi-output nonlinear dynamical system which is partially observable. To address this problem, this paper provides a set of geometrical conditions that guarantee the existence of a change of coordinates which decomposes the studied nonlinear dynamical system into two dynamical subsystems, where the first one is of the well-known output injection form. This transformed form allows us to design a simple reduced-order (Luenberger-like) observer to estimate the observable state.