This paper describes a new Artificial Neural Network (ANN), UNItary Decomposition ANN (UNIDANN), which can perform the unitary eigendecomposition of the synaptic weight matrix. It is shown both analytically and quantitatively that if the synaptic weight matrix is Hermitian positive definite, the neural output, based on the proposed dynamic equation, will converge to the principal eigenvectors of the synaptic weight matrix. Compared with previous works, the UNIDANN possesses several advantageous features such as low computation time and no synchronization problem due to the underlying analog circuit structure, faster convergence speed, accurate final results, and numerical stability. Some simulations with a particular emphasis on the applications to high resolution bearing estimation problems are also furnished to justify the proposed ANN.