Abstract: The invention concerns a method for adjusting the desired current values of shim coils of a tesseral harmonic (off axis) shim system in order, in particular in the center of the shim system, to produce as homogeneous a magnetic field as possible. Utilizing a minimal number of measuring points and appropriate linear combinations of the corresponding measurement values with and without switching on the corresponding shim coil, a simple, systematic and reliable measurement method is introduced which does not require any iterative procedure. The method can be used by itself or the desired current values can serve as starting values for a further shimming procedure.