It is known Chat the difference in the effective mass of the electron in the adjacent layers of a superlattice leads to a coupling between the electron states, which are in the parallel and perpendicular directions to the growth axis. As a consequence of this coupling, the electron band structure of the superlattice is altered. The alterations are shown in this article to be significant when a magnetic field normal to the layers is applied. Expressions for the effective mass of the electron, the width of the first miniband, and the density of states of the electrons as a function of magnetic field are obtained. Numerical results for the effective mass and bandwidth are illustrated in several diagrams.