In this paper, we propose a randomized scheduling algorithm on a fully connected homogeneous multiprocessor environment. This is a randomized version of our earlier algorithm in which we used priority of modules that was dependent on the computation and the communication times associated with the modules. First we propose a generalization of our earlier scheduling algorithm with restricted number of clusters to reduce the time complexity. Then we apply randomization to the generalized algorithm and demonstrate its superiority over our previous work. We show the complexity of our proposed algorithm as O(ab vertical bar V vertical bar(vertical bar V vertical bar+vertical bar E vertical bar)log(vertical bar V vertical bar + vertical bar E vertical bar). Here a is the number of randomization steps, and b is a limit on the number of clusters formed. If we use a and b as constants, then this gives a better complexity in comparison with the complexity of our previous algorithm that was O(vertical bar V vertical bar (2)(vertical bar V vertical bar + vertical bar E vertical bar)log(vertical bar V vertical bar+vertical bar E vertical bar)). In comparison with our previous work we get a performance improvement of up to 6.63\%; and a performance improvement of up to 12.56\% when compared with Sarkar's Edge Zeroing algorithm.