This paper introduces the implicit-IMOR method for differential algebraic equations. This method is a modification of the Index-aware model order reduction (IMOR) method proposed in our earlier papers which is the explicit-IMOR method. It also involves first splitting the differential-algebraic equations (DAEs) into differential and algebraic parts using a basis of projectors. In contrast with the explicit-IMOR method, the implicit-IMOR method leads to implicit differential and algebraic parts. We demonstrate the implicit-IMOR method using the RLC/RC networks, but it can also be applied to other problems which lead to differential-algebraic equations.