This paper deals with the problem of singularities for a class ol static-state feedback linearizable bilinear systems. For this class of nonlinear systems, the decoupling matrix is singular on an algebraic surface (which contains the origin), and this relates the static-state feedback linearization to the difficult problem of the completeness of the trajectories of the closed-loop system and/or the boundedness of the feedback laws. In this work, we give a sufficient condition under which all the trajectories of the closed-loop system are complete and the used feedback law is bounded on each of these trajectories.