This paper introduces an algorithm for independent component analysis (ICA) using explicit closed forms of two-,three-and four-dimensional antisymmetric matrix exponentials,based on which both the search direction and matrix exponentials can be directly computed in each iteration without any approximation.In addition,two errors have been corrected for the representation of four-dimensional antisymmetric matrix exponentials that were established in other works.Simulations show that the algorithm converges fast and can achieve better performance than the well-known Extended InfoMax and FastICA algorithms for mixtures of up to four independent components.