Abstract: At present, the arc-length methods are dominant tolls in structural nonlinear analysis to trace the complete paths due to its clarity in conception, convenience and reliability in calculation. During the implementation of the arc-length methods, the sign of initial loading increment parameter determines the path direction of the current tracing analysis. In this paper, the criteria for determining the sign of initial loading increment parameter are reviewed and compared, and a new criterion is presented based on the current stiffness parameter. Two examples are used to check the efficiency of the criterion, The snapping-through, snapping-back phenomena and bifurcation paths are included in one of the examples. Results show that the new criterion is simple and effective to trace the complex unstable equilibrium paths.