  We study {the} complex eigenvalues of the Wishart model defined for
nonsymmetric correlation matrices. The model is defined for two statistically
equivalent but different Gaussian real matrices, as
$\mathsf{C}=\mathsf{AB}^{t}/T$, where $\mathsf{B}^{t}$ is the transpose of
$\mathsf{B}$ and both matrices $\mathsf{A}$ and $\mathsf{B}$ are of dimension
$N\times T$. We consider {\it actual} correlations between the matrices so that
on the ensemble average $\mathsf{C}$ does not vanish. We derive a loop equation
for the spectral density of $\mathsf{C}$ in {the} large $N$ and $T$ limit where
the ratio $N/T$ is finite. The actual correlations changes the complex
eigenvalues of $\mathsf{C}$, and hence their domain from the results known for
the vanishing $\mathsf{C}$ or for the uncorrelated $\mathsf{A}$ and
$\mathsf{B}$. Using the loop equation we derive {a} result for the contour
describing the domain of {the} bulk of the eigenvalues of $\mathsf{C}$. If the
nonvanishing-correlation matrix is diagonal with the same element $c\ne0$, the
contour is no longer a circle centered at origin but a shifted ellipse. In this
case, the loop equation is analytically solvable and we explicitly derive {a}
result for the spectral density. For more general cases, our analytical result
implies that the contour depends on its symmetric and anti-symmetric parts if
the nonvanishing-correlation matrix is nonsymmetric. On the other hand, if it
is symmetric then the contour depends only on the spectrum of the correlation
matrix. We also provide numerics to justify our analytics.
