An Orthogonal Least Squares (OLS) based feature selection method is proposed for both binomial and multinomial classification. The novel Squared Orthogonal Correlation Coefficient (SOCC) is defined based on Error Reduction Ratio (ERR) in OLS and used as the feature ranking criterion. The equivalence between the canonical correlation coefficient, Fisher's criterion, and the sum of the SOCCs is revealed, which unveils the statistical implication of ERR in OLS for the first time. It is also shown that the OLS based feature selection method has speed advantages when applied for greedy search. The proposed method is comprehensively compared with the mutual information based feature selection methods and the embedded methods using both synthetic and real world datasets. The results show that the proposed method is always in the top 5 among the 12 candidate methods. Besides, the proposed method can be directly applied to continuous features without discretisation, which is another significant advantage over mutual information based methods.