This paper addresses the small-size problem in Fisher Discriminant Analysis. We propose to use wavelet transform for preliminary dimensionality reduction and use a two-parameter regularization scheme for the within-class scatter matrix. The novelty of the proposed method comes from: (1) Wavelet transform with linear computation complexity is used to carry out the preliminary dimensionality reduction instead of employing a principal component analysis. The wavelet filtering also acts as smoothing out noise. (2) An optimal solution is found in the full space instead of a sub-optimal solution in a restricted subspace. (3) Detailed analysis for the contribution of the eigenvectors of the within-class scatter matrix to the overall classification performance is carried out. (4) An enhanced algorithm is developed and applied to face recognition. The recognition accuracy (rank 1) for the Olivetti database using only three images of each person as training set is 96.7859%. The experimental results show that the proposed algorithm could further improve the recognition performance.