Motivated by a singular technique for root-finding, two Newton's methods are generalized to a class of iteration formats, on the basis of which, a modification of the Newton's method solving non-linear equations with singular Jacobian is presented.Firstly, the new rule is described and its convergence order is analyzed. The modified singular method requires one function and one first derivative evaluations per step.Then, numerical examples demonstrate the faster convergence achieved with this modification than Newton's method and some singular schemes.Finally, two practical problems are given to illustrate the effectiveness of the proposed method.