Cepstral mean subtraction (CMS) and cepstral normalization (CN) have been popularly used to normalize the first and the second moments of cepstral coefficients, and proved to be very helpful for robust speech recognition [1,2]. In this paper, a unified formulation for Higher Order Cepstral Moment Normalization (HOCMN) is developed by extending the concept of CMS and CN to orders much higher than three. A whole family of normalization techniques for different orders is thus proposed. Preliminary experimental results based on Aurora 2.0 showed that the recognition accuracy can be significantly improved with this approach under all noisy conditions. For example, HOCMN [1,5,100] (normalization of the first, fifth and 100-th order cepstral moments) is shown to offer an error rate reduction of 32.83% as compared to the conventional CN with a full-utterance processing interval, or an error rate reduction of 20.78% as compared to CN with a segmental processing interval.