This paper introduces a new multicarrier system using a low computational complexity transform that combines the Walsh-Hadamard transform (WHT) and the discrete Fourier transform (DFT) into a single fast orthonormal unitary transform. The proposed transform is used in a new orthogonal frequency division multiplexing ( T-OFDM) system, leading to a significant improvement in bit error rate (BER) and reasonable reduction in the peak-to-average power ratio (PAPR). Use of the proposed transform with OFDM has been found to attain high frequency diversity gain by combining all data samples resulting in the transmission over many subcarriers. Consequently, the detrimental effect arising from channel fading on the subcarrier power is minimized. Theoretical analysis of the uncoded T-OFDM performance over additive white Gaussian noise (AWGN), flat fading, quasi-static (fixed within the entire period of OFDM symbol transmission) frequency selective fading channel models with zero-forcing (ZF) and minimum mean square error (MMSE) equalizers is presented in this work. Moreover, the low superposition of the subcarriers passing through the T-transforms leads to a reduction in the high peak of the transmitted signal whilst preserving the average transmitted power and data rate. Analytical results confirmed by simulations demonstrated that the proposed T-OFDM system achieves lower PAPR and the same BER over AWGN and flat fading channels. Compared to OFDM, T-OFDM is found to have better BER when MMSE equalizer is used, but slightly worse when ZF equalizer is used.