Abstract: This paper introduces a new low-computational method for approximating the skew-symmetric and skew-Hermitian matrix exponential. Our method belongs to the splitting methods, which we modify and combine with new low-cost analytic formula for sparse skew-symmetric and skew-Hermitian matrix exponential, similar to the Euler-Rodrigues formula, well known for the skew-symmetric matrices in R^3. Our new approximation procedure for skew-symmetric (skew-Hertmitian) matrix exponential that we use is computationally very cheap, which ensures high speed of algorithms using this operation in their structure. To evaluate this approximation method we used it for the optimization problem of Independent Component Analysis (ICA) type. The results are compared to other known ICA algorithms such as well known Infomax and JADE. The average increase in convergence speed in the studied range of the number of source images was approximately 7% compared to the second fastest ICA algorithm using the standard and universal matrix exponential formula. High quality of separation was also obtained, comparable to well-known ICA algorithms such as Infomax or JADE.. Obtained results confirm the effectiveness of the proposed method in technical applications and indicate potential use in on-line applications.