This paper presents a new data predistortion technique with memory to compensate for the nonlinearities of high-power amplifiers (HPA`s) in digital radio systems employing QAM signal formats. In contrast with the conventional data predistortion technique which is designed to reduce nonlinearity of memoryless HPA`s, the proposed technique in this paper compensates not only for nonlinear warping of the signal constellation but also for clustering of the signal points caused by transmitter pulse sharping filter with memory. A practical implementation method which can reduce the size of memory at the predistortion stage is described by utilizing symmetry of QAM constellation format and Modulo-4 operation.