In this talk, we consider a data matrix X = (x_1, ..., x_M) where all of the M columns are i.i.d. samples being N dimensional Gaussian of mean zero and covariance matrix Sigma. Here Sigma is of finite-rank perturbation of the identity matrix. This is the "spiked population model" first proposed by Johnstone. We consider the sample covariance matrix S = XX'/M. If some eigenvalues of Sigma deviates from one by a large amount, then it will pull sample eigenvalues out of the Marcenko-Pastur sea. These outstanding sample eigenvalues will form packs according to the algebraic multiplicity of the true eigenvalue. Bai proved that each pack will behave like the spectrum of a GOE matrix. In this talk we further prove that different packs are asymptotically independent, hence complete the characterization of the joint distribution of outstanding sample eigenvalues.