We study Principal Component Analysis (PCA) in the setting where a part of the corrupting ``noise" is correlated with the true data (correlated-PCA). Such corruption is often called ``data-dependent noise". We provide a guarantee for the most commonly used PCA solution, simple eigenvalue decomposition (EVD) of the empirical covariance matrix. To our best knowledge, most existing results that study the simple EVD solution to PCA assume that the true data and the corrupting noise are uncorrelated. This is valid in practice often, but not always. We first studied correlated-PCA in a 2016 NIPS paper. This talk will remove two key limitations of that work.