We derive a set of weights for the storage of correlated biased patterns in a fully connected net. The connections are built from the eigenvectors or principal components of the pattern correlation matrix. We present simulation results that show these connections are capable of storing up to N random patterns in a network of N spins. Basins of attraction are also investigated via simulation and we compare them with those of the Psuedo-Inverse rule. Finally, we discuss a biologically plausible method of constructing such a connection matrix.