A new family of least-change secant methods for solving systems of nonlinear algebraic equations is introduced. At each iteration of the methods of this family, the matrix $B_k $ is represented as a product of the form $A_k^{ - 1} R_k $, where the matrices $A_k $ and $R_k $ have a determined structure and $A_{k + 1} $, $R_{k + 1} $ are chosen by the use of a least-change secant rule. The first and second methods of Broyden [Math. Comp., 19 (1965), pp. 577–593], [Math. Comp., 25 (1971), pp. 285–294], and the methods of Schubert [Math. Comp., 24 (1970), pp. 27–30], Johnson and Austria [SIAM J. Numer. Anal., 20 (1983), pp. 315–325], and Chadee [Tech. Report SOL 85-8, Dept. of Operations Research, Stanford University, Stanford, CA, 1985] are members of this family. Local and superlinear convergence results are proved, and particular members of the family that seem to be of practical usefulness are introduced.