Natural image matting is a task to estimate fractional opacity of foreground layer from an image. Many matting methods have been proposed, and most of them are trimap-based. Among these methods, closed-form matting offers both trimap-based and scribble-based matting. However, the closed-form method causes significant errors at background-hole regions due to over-smoothing. In this paper, we identify the source of the problem and propose our solution to enhance the closed-form method. Experiments show that our enhanced method can improve the accuracy for trimap-based images and obtain similar result to the closed-form method for scribble-based matting.