The relatively slow progress in both analytical and numerical work on the structure of the pulsar magnetosphere calls for a reformulation of the equations governing the magnetosphere. Since the set of equations for the pulsar magnetosphere are nonlinear anyway, one should not hesitate to use nonlinear representations for the field intensities and the current from the very beginning. Those nonlinear representations can be chosen to fulfill certain equations automatically and are therefore more adapted to the problem. The aligned rotator was formulated to some extent in this way by Schmalz et al. (1979). We formulate here the general problem and use for this the calculus of differential forms and some theorems concerning the normal form of forms (= representation of a form with a minimal number of scalar functions and their gradients). In the language of forms Maxwell's equations read where F is the field intensity 2-form and j the current 3-form. The first equation states that F can be derived from a 1-form A: F = dA, the usual vector potential. A consequence of the second equation is dj = 0, the continuity equation for the current. Now since j is a simple closed 3-form, it can be represented by three scalar functions ⊘,χ,Ψ in the following way which obviously satisfies dj = 0. This is the normal form of the 3-form with the properties mentioned above.