The literature on codes for write-once memories (WOM) has been growing steadily in recent years. In this paper, a new method for constructing womcodes is presented. On the basis of the numerical analysis and the computer simulations related to the performance of the proposed womcodes, we show that the codes have the rates higher than any other known womcodes. The upper bounds on the rates of the codes are obtained as well. We also show that, by combining the proposed womcodes with other womcodes known previously, we can significantly improve the utilization efficiency of WOM.