We report on high-resolution friction force microscopy on a stepped NaCl(001) surface in ultrahigh vacuum. The measurements were performed on single cleavage step edges. When blunt tips are used, friction is found to increase while scanning both up and down a step edge. With atomically sharp tips, friction still increases upwards, but it decreases and even changes sign downwards. Our observations extend previous results obtained without resolving atomic features and are associated with the competition between the Schwöbel barrier and the asymmetric potential well accompanying the step edges.