Gauss quadrature is a popular approach to approximate the value of a desired integral determined by a measure with support on the real axis. Laurie proposed an -point quadrature rule that gives an error of the same magnitude and of opposite sign as the associated -point Gauss quadrature rule for all polynomials of degree up to . This rule is referred to as an anti-Gauss rule. It is useful for the estimation of the error in the approximation of the desired integral furnished by the -point Gauss rule. This paper describes a modification of the -point anti-Gauss rule, that has nodes and gives an error of the same magnitude and of opposite sign as the associated -point Gauss quadrature rule for all polynomials of degree up to for some . We refer to this rule as a generalized anti-Gauss rule. An application to error estimation of matrix functionals is presented.