J. Comp. Math., Volume 20. The Solvability Conditions For Inverse Eigenvalue Problem Of Anti-Bisymmetric Matrices Dong Xiu Xie 1, Xi Yan Hu 2, Lei Zhang 31 Beijing Institute of Machinery Industry, Beijing 100085, China 2 Department of Applied Mathematics, Hunan University, Changsha 410082, China 3 Hunan Computing Center, Changsha 410012, China Abstract This paper is mainly concerned with solving the following two problems: Problem I. Given X \in C_n \times m, \Gamma = diag(\lambda1, \lambda2, \dots, \lambda m) \in Cm\times m. Find A \in ABSRn\times n such that where ABSRn\times n is the set of all real n \times n anti-bisymmetric matrices. Key words: Eigenvalue problem; Norm; Approximate solution.