Unique Word Orthogonal Frequency Division multiplexing (UW-OFDM) is a variant of the multicarrier technique that has shown better bit error performance compared to cyclic prefixed (CP-)OFDM. Like other multicarrier techniques, UW-OFDM suffers from the high peak-to-average-power ratio (PAPR) problem, which is an obstacle ahead of practical implementation of UW-OFDM. In this letter, the generator matrix, which is inherent to UW-OFDM, is not only used to create the specific UW-OFDM system, but also to reduce the PAPR. To do so, a suitable optimization problem is developed, and solved using the Procrustes method. The main advantage of the proposed method is that the built-in generator matrix should be calculated only once for each system setting, and the PAPR reduction (PAPR-R) is achieved without any overhead redundancy. Simulation results are provided for evaluating the PAPR-R performance of the proposed method.