As the cluster number of texture in an image is always unknown, the unsupervised classification is more valuable than the supervised classification. Based on th e concept of a good cluster which should have the minimum intra-cluster distance and the maximum inter-clusters distance, the ratio of intra-cluster to inter-cl uster distance is applied as the validity function. However, the increase of ini tial cluster number will influence the sum of cluster diameters and the inter-cl uster separation distance. Therefore the maximum cluster diameter and minimum in ter-cluster separation distance are provided instead, which is influenced by the initial cluster number more slightly and shows the essential of the cluster str ucture. Due to the relationship of FCM convergent speed with the initial cluster number, the convergent speed is introduced as the penalization factor to the va lidity function and a new validity function nRII is proposed. Compared with othe r validity functions, the nRII validity function can effectively prevent the ove r-clustering problem and give out a more exact estimation of the cluster number.