The symmetric ABS method is considered for solving matrix equations. A remarkable feature of this method is that, for a given matrix equation, it provides a Solution in closed form that has interesting least change properties. This result is exploited to establish secant-type updates by solving certain least change problems. Both Broyden's updates for nonlinear systems of equations and the weak secant updates for unconstrained optimization proposed by Dennis and Wolkowicz are extended to the multiple case