The major drawback of OFDM transmission is the large envelope fluctuation which is qualified as Peak to Average Power Ratio. Since power amplifier is used at the transmitter, so as to operate in a perfectly linear region the operating power lies below the available power. For reduction of this PAPR lot of algorithms have been developed. A uniformly distributed nonlinear companding scheme efficiently reduces PAPR with a low Bit Error Rate (BER). However, the uniformly distributed companding scheme cannot perform variably to satisfy the different performance requirements for the systems. Therefore, this work proposes a novel scheme that transforms the OFDM signals into a trapezium distribution. The uniformly distributed companding scheme is a special case of the proposed scheme. The general formulas of the proposed scheme are derived and the trade-off between PAPR reduction and BER performance is achieved by setting the value of a parameter. Then, the simulation results show the PAPR reduction and the BER over the AWGN and multipath channels, indicating that the proposed scheme provides a favourable trade-off between the Papr Reduction and the BER.