This paper describes a new high resolution algorithm for the two-dimensional (2-D) frequency estimation problem, which, in particular, is noise insensitive in view of the fact that in many practical applications the contaminated noise may not be white noise. For this purpose, the approach is set in the context of higher-order statistics (HOS), which has demonstrated to be an effective approach under a colored noise environment. The algorithm begins with the consideration of the fourth-order moments of the available 2-D data. Two auxiliary matrices, constituted by a novel stacking of the diagonal slice of the computed fourth-order moments, are then introduced and through which the two frequency components can be precisely determined, respectively, via matrix factorizations along with the subspace rotational invariance (SRI) technique. Simulation results are also provided to verify the proposed algorithm.