<正> As for higher singularity integral equation:its solvability conditions have been investigated in reference [1]. In reference [2], the direct solutionmethod has been discussed. In this paper, we will discuss a kind of method of directly finding solution.As n=2, the equation (1) equivalent to the following;here L is a simple closed curve; D+, D-, are the inner-field and outer-field respectively, which are sur-rounded by curve L, we need (t)∈ H1 (L).Assume that Nx(z,ζ) =(kv(z,ζ)-kv(z,ζ))/a2(z)+b2(z) is meromorphic on × ,v = 1,2,3. Furthermore it