Summary: This work presents an effective procedure devised to implement the time discontinuous Galerkin method for linear dynamics. In particular, the method with piecewise linear time interpolation is considered. The procedure is based on a simple and low-cost iterative scheme, which is designed not as a mere solution algorithm, but rather as a method to generate improved approximations to the exact solution. The corrected solutions inherit the desired stability and dissipative properties from the target solution, while accuracy is improved by iterations. Indeed, no more than two iterations are shown to be needed. The resultant algorithm leads to remarkable computational savings and can be easily implemented into existing finite element codes. Numerical tests confirm that the present procedure possesses many attractive features for applications to dynamic analysis.