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In this paper, a new companding transform for reduction in peak to average power ratio of OFDM signals is proposed. Linearity and existence of inflection points, which are key features of two previous works, are maintained in the proposed transform. However, unlike the previous works, the proposed transform does not cause abrupt jumps in the signal, hence leads to better spectral characteristics. Furthermore, the proposed method improves the BER performance of OFDM system compared to the previous methods. Computer simulations verify that the signal resulting from the proposed transform has less out-of-band radiation (better spectral characteristics), better BER performance, and lower PAPR compared to the previous works.