In all systems simulation, random variates are considered as a main factor and based of simulation heart. Actually, randomization is inducted by random variates in the simulation. Due to the importance of such a problem, a new method for generation of random variates from continuous distributions is presented in this paper. The proposed algorithm, called uniform fractional part (UFP) is simpler and more efficient compared with other methods of random variates generation. Despite useful consequences, this algorithm has several shortcomings such as 1) being approximate, 2) not accessibility of the inverse of cumulative density function (CDF) for all distributions in order to determine the cut-off points and 3) truncating the tails of infinite distributions, which all of the aforementioned shortcomings reduce the precision and speed of the algorithm. The main goal of this research is proposing the improved version of this algorithm (IUFP) through recognizing its deficiencies.