We consider the semilinear heat equation in a bounded domain of R^m. We prove the null controllability of the system with a finite number of constraints on the normal derivative, when the control acts on a bounded subset of the domain. First, we show that the problem can be transformed into a null controllability problem with constraint on the control, for a linear system. Then, we use an appropriate observability inequality to solve the linearized problem. Finally, we prove the main result by means of a fixed-point method.