The multicanonical sampling and jump walking methods are combined to provide a new, effective means of overcoming quasiergodicity in Monte Carlo simulations. In this new method, configurations generated during a long multicanonical sampling are stored infrequently and a modified jump walking procedure is implemented using this set of configurations to sample phase space at low temperature. Multicanonical jump walking, as this new method is called, is compared with regular jump walking and with straight multicanonical ensemble sampling on two systems: a one-dimensional random potential and an Ar-13 cluster. It is shown that for the same number of MC steps, the multicanonical jump walking method more efficiently samples the phase space than either the regular jump walking or the pure multicanonical ensemble sampling method.