  We consider the $\top$-Stein equation $X = AX^\top B + C$, where the operator
$(\cdot)^\top$ denotes the transpose ($\top$) of a matrix. In the first part of
this paper, we analyze necessary and sufficient conditions for the existence
and uniqueness of the solution $X$. In the second part, a numerical algorithm
for solving $\top$-Stein equation is given under the solvability conditions.
