Local search (LS) methods heuristically find a solution for constraint satisfaction problems (CSP). LS starts the search for a solution from a random assignment. LS then examines the neighbours of this assignment to determine a better neighbour valuation to move to. It repeats this process of moving from the current assignment to a better assignment until it finds a solution that satisfies all constraints. ICM considers some of the constraints as hard constraints that are always satisfied. In this way, ICM reduces the possible neighbours in each move and hence the overall search space. ICM chooses the hard constraints in such away that the space of valuations that satisfies these constraints is connected in order to guarantee that a local search can reach any solution from any valuation in this space. In this paper, we incorporate ICM into one of the most recent local search algorithm, ESG, and we show the improvement of the new algorithm. We ran this algorithm in different SAT problems.