The relationship between Walsh transform of a Boolean function and the orthogonality of some columns of its support table is investigated. This result improves the characterization of the orthogonality of Orthogonal array (OA). Stinson and Massey gave two construction methods of linear resilient functions, one is to use linear code, the other is to utilize the large set of orthogonal arrays and right cosets. And another major contribution is to show the equivalence of two methods