In this paper, a new fast and low complexity transform is introduced for orthogonal frequency division multiplexing (OFDM) wireless systems. The new transform combines the effects of fast complex-Walsh-Hadamard transform (CHT) and the fast Fourier transform (FFT) into a single unitary transform named in this paper as the complex transition transform (CTT). The development of a new algorithm for fast calculation of the CT transform called FCT is found to have all the desirable properties such as in-place computation, simple indexing scheme and considerably lower arithmetic complexity than existing algorithms. Furthermore, a new OFDM system using the FCT algorithm is introduced and its performance has been evaluated. The proposed CT-OFDM achieves a noticeable reduction in peak-to-average-power-ratio (PAPR) and a significant improvement in the bit-error-rate (BER) performance compared with the conventional OFDM.