Clustering in data mining is a discovery process that groups similar objects into the same cluster. Various clustering algorithms have been designed to fit various requirements and constraints of application. In this paper, we study several k-medoids-based algorithms including the PAM, CLARA and CLARANS algorithms. A novel and efficient approach is proposed to reduce the computational complexity of such k-medoids-based algorithms by using previous medoid index, triangular inequality elimination criteria and partial distance search. Experimental results based on elliptic, curve and Gauss-Markov databases demonstrate that the proposed algorithm applied to CLARANS may reduce the number of distance calculations by 67% to 92% while retaining the same average distance per object. In terms of the running time, the proposed algorithm may reduce computation time by 38% to 65% compared with the CLARANS algorithm.