Clustering is an important data mining problem. The k-means algorithm is best suited for implementing this operation of its efficiency in clustering large data sets. However, working only on numeric values limits its use in data mining because data sets in data mining often contain categorical values. In this paper we introduce an algorithm, called k-priorities which is based on the k-means algorithm but removes the numeric data limitation whilst preserving its efficiency. In this algorithm, objects are clustered against k-priorities in order to maximize the accurancy. We introduce new dissimilarity measures to deal with categorical data sets by replace means of cluster with priority. Tested with the MUSHROOM data sets the k-priorities has shown a good performance for the two aspects (accurancy, complexity).