In this paper we present a new algorithm for the computation of the minimal Geršgorin set that can be considered an extension of the results from [5]. While the general approach to calculation of the boundary of the minimal Geršgorin set is kept, the core numerical calculation is changed. Namely, the problem is formulated in such a way that the eigenvalue computations are replaced by LU decompositions, allowing the algorithm to be used for larger matrices more efficiently. To illustrate the benefits, we compare both algorithms on several test matrices,