A new light is thrown on the Portnoff [1] speech signal time-scale modification algorithm. It is shown in particular that the Portnoff algorithm easily accommodates expansion factors bigger than 2 without causing reverberation nor chorusing. The modified Portnoff algorithm, which draws on spectral modification techniques due to Seneff [2], has been tested on several speech signals. The quality of the synthesized signal is totally satisfactory even for big expansion factors. The article gives a brief summary of the Portnoff algorithm and spells out the modifications introduced. It is shown that the phase unwrapping procedure constitutes a crucial point of the algorithm.