This paper proposes a new nonlinear companding scheme with reduced symbol error rate (SER) that can be used to reduce peak-to-average power ratio (PAPR) in orthogonal frequency division multiplexing (OFDM) systems. The proposed system outperforms conventional companding systems using the same nonlinear companding functions with respect to SER without impairing PAPR reduction capability. The proposed system estimates a few autoregressive moving average (ARMA) model parameters of the difference signal between the companded and uncompanded OFDM envelopes and passes these parameters to the receiver. Upon receiving the ARMA model parameters, the receiver regenerates the difference signal and then adds it to the received companded OFDM envelope to recover the uncompanded OFDM signal. The traditional schemes employ decompanding process instead to reconstruct the uncompanded OFDM signal. Mathematical proofs and simulation results for three typical nonlinear companding functions show that, under mild sufficient conditions, the proposed scheme outperforms the conventional schemes with respect to SER performance without impairing PAPR reduction capability.