A method for enclosing the solution set of a system of interval linear equations with unit midpoint interval matrix is proposed. It is a variant of the interval Gauss-Seidel method employing some quantities appearing in the interval arithmetic formulas for the interval hull by S. Ning and R. B. Kearfott [SIAM J. Numer. Anal. 34, No. 4, 1289–1305 (1997; Zbl 0889.65022)].