In this paper we study the residual proton-neutron interactions and make use of the systematics of these interactions to describe experimental data of nuclear masses and to predict some of the unknown masses. The odd-even effect staggering of the residual proton-neutron interaction between the last proton and the last neutron is found and argued in terms of pairing interactions. Two local mass relations, which work very accurately for masses of four neighboring nuclei, are discovered. The accuracy of our predicted masses for medium and heavy nuclei is competitive with that of the AME2003 extrapolations, with the virtue of simplicity.