The main limitation in employing orthogonal frequency division multiplexing (OFDM) system is high peak-to-average power ratio (PAPR) of the transmitted signal. A new nonlinear companding algorithm that transforms the OFDM signals into the desirable statistics form defined by a linear piecewise function is proposed. The more adjustability in companding form and an effective trade-off between the PAPR and bit error rate (BER) performances can be obtained by introducing an inflexion point and the variable slopes in the target probability density function. Theoretical analyses for this algorithm is presented and expressions regarding the achievable signal attenuation factor and transform gain are produced. The selection criteria of transform parameters focusing on its robustness and performance aspects are also examined. The conferred theoretical analyses are well verified via computer simulations.