This paper is concerned with an iterative algorithm for solving the minimum Frobenius norm residual problem: 〖WTBX〗min〖JB(=〗〖JB((〗〖HL(1〗〖WTHX〗A1XB1+C1X〖TX-〗D1A2XB2+C2X〖TX-〗D2〖HL)〗〖JB))〗-〖JB((〗〖HL(1〗M1M2〖HL)〗〖JB))〗〖JB)=〗, 〖WT〗where 〖WTHX〗X〖WT〗 is a Hermite bisymmetric matrix which satisfies 〖WTHX〗X=X〖WTBX〗H=〖WTHX〗S〖WTBX〗n〖WTHX〗XS〖WTBX〗n〖WT〗. We can get the solution with finite iteration steps in the absence of roundoff errors for any initial Hermite bisymmetric matrix 〖WTHX〗X〖WT〗0 by this algorithm. Finally, a numerical example is given to illustrate the effectiveness of the proposed method.