The most commonly used formulations of non-linear analyses are the total or updated Lagrangian formulations, which have been incorporated into many commercial finite element packages. However, for a special class of nonlinear problems, namely, large displacements and rotations but moderate strains, the Co-rotational formulation can be employed to further simplify the Lagrangian formulations. A lot of iterative procedures for tracing the nonlinear equilibrium paths have been devised in nonlinear analysis. However in some cases, there are issues still existing so far, especially in geometric nonlinear problems possessing the snap-through and/or snap-back properties. Thus, it has indeed improvement on the classical ones to achieve an effective solution. A novel constraint equation which is linear, simple and low cost of iteration compared with the classical arclength algorithm is suggested in this paper. Several numerical examples are tested to verify the accuracy and performance of the proposed approach.