  A generalized tournament matrix $M$ is a nonnegative matrix that satisfies
$M+M^{t}=J-I$, where $J$ is the all ones matrix and $I$ is the identity matrix.
In this paper, a characterization of generalized tournament matrices with the
same principal minors of orders $2$, $3$, and $4$ is given. In particular, it
is proven that the principal minors of orders $2$, $3$, and $4$ determine the
rest of the principal minors.
