K-means algorithm is one of the most popular algorithms for data clustering. With this algorithm, data of similar types are tried to be clustered together from a large data set with brute force strategy which is done by repeated calculations. As a result, the computational complexity of this algorithm is very high. Several researches have been carried out to minimize this complexity. This paper presents the result of our research, which proposes a modified version of k-means algorithm with an improved technique to divide the data set into specific numbers of clusters with the help of several check point values. It requires less computation and has enhanced accuracy than the traditional k-means algorithm as well as some modified variant of the traditional k-Means.