In this paper, we propose a new algorithm for learning overcomplete dictionaries. The proposed algorithm is actually a new approach for optimizing a recently proposed cost function for dictionary learning. This cost function is regularized with a term that encourages low similarity between different atoms. While the previous approach needs to run an iterative limited-memory BFGS (l-BFGS) algorithm at each iteration of another iterative algorithm, our approach uses a closedform formula. Experimental results on reconstruction of a true underlying dictionary and designing a sparsifying dictionary for a class of autoregressive signals show that our approach results in both better quality and lower computational load.