We apply the Kerman-Klein method of quantization, an approach based on Heisenberg matrix mechanics, to the Skyrme model. In this approach the operator equations of motion and kinematical constraints are evaluated within an appropriately chosen Hilbert space, and the resulting set of c-number equations is solved to determine the values of matrix elements of the field operators. These values permit predictions for physical observables. The Kerman-Klein method allows symmetries to be maintained throughout the computation, a property shared with methods based on variation after projection techniques. In this report we concentrate on the quantization of the rotational zero modes of a Skyrmion. We show that the restoration of rotational symmetry leads to a state that is larger than the nucleon and to a modification of the values of observables. © 1993 The American Physical Society.