The finite element time discretization is utilized to develop a new direct integration method. The derived recurrence formula is implicit and self-starting. There are no undetermined parameters which are often used to control stability and accuracy in the traditional direct time integration methods. The method is analytically shown to be unconditionally stable and second-order accurate. The test with a single degree-of-freedom linear model has supported the analysis of convergence and errors. It has been shown that the proposed method gives consistently better response history than the two well-known methods even with larger time steps. A two degree-of-freedom Hertzian impact model is solved to show its performance for a typical nonlinear problem. It is concluded that the proposed method works very well with useful properties as expected.