We consider a Schrodinger operator with a constant magnetic field in a half 3-dimensional space, with Neumann type boundary conditions. It is known from the works by Lu-Pan and Helffer-Morame that the lower bound of its spectrum is less than the intensity b of the magnetic field, provided that the magnetic field is not normal to the boundary. We prove that the spectrum under b is a finite set of eigenvalues (each of infinite multiplicity). In the case when the angle between the magnetic field and the boundary is small, we give a sharp asymptotic expansion of the number of these eigenvalues.