The quasi-Newton equation has played a central role in the quasi-Newton methods forsolving systems of nonlinear equations and/or unconstrained optimization problems. Instead,Pan suggested a new equation,and showed that it is of the second order while the traditional of the first order,in certain approximation sense [12]. In this paper,we make a generalization of the two equations to include them as special cases. The generalized equation is analyzed,and new updates are derived from it. A DFP-like new update outperformed the traditional DFP update in computational experiments on a set of standard test problems.