This paper proposes a second-order implicit constraint enforcement method which yields enhanced controllability compared to a first-order implicit constraints enforcement method. Although the proposed method requires solving a linear system twice, it yields superior accuracy from the constraints error perspective and guarantees the precise and natural movement of objects, in contrast to the first-order method. Thus, the proposed method is the most suitable for exact prediction simulations. This paper describes the numerical formulation of second-order implicit constraints enforcement. To prove its superiority, the proposed method is compared with the firstorder method using a simple two-link simulation. In this paper, there is a reasonable discussion about the comparison of constraints error and the analysis of dynamic behavior using kinetic energy and potential energy.