In this paper, we propose an unsupervised genetic clustering algorithm, which produces a new chromosome without any conventional genetic operators, and instead according to the gene reproducing probabilities determined by Markov chain modeling. Selection of cluster centers from the dataset enables construction of a look-up table that saves the distances between all pairs of data points. The experimental results show that the proposed algorithm not only solves the premature problem to provide a more stable clustering performance in terms of number of clusters and clustering results, but also improves the time efficiency.