Research on preconditioning Toeplitz matrices with circulant matrices has been active recently. The preconditioning technique can be easily generalized to block Toeplitz matrices.That is, for a block Toeplitz matrix T consisting of N N blocks with M M elements per block, a block circulant matrix R is used with the same block structure as its preconditioner. In this research, the spectral clustering property of the preconditioned matrix R-1T with T generated by two-dimensional rational functions T(z,,zy) of order (p:r,q:,pu,qv) is examined. It is shown that the eigenvalues of R-1T are clustered around unity except at most O(M/u + N"/) outliers, where max(p, q) and max(p, qy). Furthermore, if T is separable, the outliers are clustered together such that R-1T has at most (2/x + 1)(2 + 1) asymptotic distinct eigenvalues. The superior convergence behavior of the preconditioned conjugate gradient (PCG) method over the conjugate gradient (CG) method is explained by a smaller condition number and a better clustering property of the spectrum of the preconditioned matrix R-1T.