This paper proposes a modified spectral subtraction method for the enhancement of noisy speech. The conventional spectral subtraction method involves two phases. In the first phase the average estimate of the noise spectrum is subtracted and the second phase involves several modifications to reduce the signal level, predominantly in nonspeech regions. The present work implements the first phase as it is and replaces the second phase by a new approach. For speech corrupted by additive noise, kurtosis and energy values will be high in speech regions compared to nonspeech regions. This property is exploited in deriving a weight function. The Linear Prediction (LP) residual of the spectral subtracted speech signal is modified by the weight function. The enhanced speech signal is synthesized from the modified LP residual and the all pole filter derived from the spectral subtracted speech signal.Index Terms-speech enhancement, spectral subtraction and kurtosis.