can we get equal orthogonal bases by searching the optimal approximation to the multi-orthogonal bases? and our searching methods is basing on a generalization of the non-archimedean norm spaces. for more details, you can refer to the url :http://vixra.org/abs/1302.0007 (page 2-13),the paper named “non-archimedean analysis-the application of symmetric methods” our step is as follow: 1.generalize the symmetric norms to n dimension. 2.estimate the max and min value of the parameter a. 3.add or substract terms at the right hand side of the inequality(which we get by the estimate in step 2) to achieve the optimal approximate towards the bases, which relate step 1 and step 2,then we can get equal orthogonal bases under the condition of limit and the estimate is optimal.