This article focuses on a method to relocate the robotic fingertips on the surface of the object when the fingertips instantaneously hold the object under precision grasp. Precision grasp involves holding the object using fingertips. Finger gaiting involves repositioning the fingertips on the surface of the object and then manipulation of the object. During repositioning, one contact point leaves the object surface and recontacts at the other point. A metric is defined on the set of feasible grasp configurations to limit deviation from force closure during repositioning of the fingertips. Then, a manipulability-based metric is described to search for the optimal goal grasp states on the object’s surface. The manipulability-based metric is used to search the grasp state to relocate the contacts, such that the range of object motion is increased.