The work objective is speeding the covariance matrix converter of the adaptive antenna array interference by reducing the number of operations performed. A problem of developing an aprior information inversion algorithm relying on the Hermitian nature of the reversible matrix is considered. The proposed algorithm is based on a bordering method in contrast to the well-known algorithms based on method of Gaussian-Jordan elimination. Because of complexity and a large operation number, Gaussian-Jordan method does not allow realizing the real time signal processing in computing systems of the adaptive antenna arrays that are widely used in communication, radiolocation, and radio navigation systems. The proposed algorithm extends a well-known bordering method by taking into account Hermitian nature of the covariance interference matrix, and allows developing an algorithm based on the recursive relations. An obtained gain in amount of calculation is no less than 25% comparing to the method of Gaussian-Jordan elimination. The calculation amount decrease and a more simple form of relations used for the matrix inversion algorithm elaboration allow developing a more simple design of the adaptive antenna array processor for the matrix inversion.