Two sets of range data representing feature points on a rigid object at two time instances can be used to estimate motion parameters of the object. In general, the point correspondence between the two sets are matched first and then the motion parameters are estimated by solving equations which govern the corresponding points. A new method for determining the point correspondences and the motion parameters is presented. An algorithm which gives four candidate matrices for the object rotation from the three-dimensional (3-D) data without point correspondence is derived. The point correspondences and motion parameters can then be determined by the proper selection of the rotation matrix. If the data contain noise, the algorithm provides a rough estimation of the motion parameters and serves as the basis for matching the point correspondences in the two range-data sets. Some simulation results are shown to illustrate the efficiency and accuracy of the algorithm.