An estimator of the covariance matrix in signal processing is derived when the noise covariance matrix is arbitrary based on the method of maximum likelihood estimation. The estimator is a continuous function of the eigenvalues and eigenvectors of the matrix Σ̂11/2SΣ̂11/2, where S is the sample covariance matrix of observations consisting of both noise and signals and Σ̂1 is the estimator of covariance matrix based on observations consisting of noise only. Strong consistency and asymptotic normality of the estimator are briefly discussed.