In this article, the elimination of ambiguity of a joined coprime array has been examined, with a focus on such of its properties as large aperture size and complete degree of freedom (DOF). The existing methods suffer from a high degree of computation complexity due to the loss constant characteristic and high peak searching. Therefore, in this paper, a DOA estimation method for a jointed coprime array, characterized by a low degree of computational complexity, is proposed. The variance of the diagonal eigenvalues of the estimated covariance matrix is designed to enhance the accuracy of the covariance matrix of the joined coprime array. Then, the Capon beamforming methods is employed for peak searching. The simulation shows that the proposed method accomplishes accurate estimation with shorter computation times and fewer operations compared to other DOA estimation methods.