  In this note, we consider the uncrossing game for a skew-supermodular
function $f$, which is a two-player game with players, Red and Blue, and
abstracts the uncrossing procedure in the cut-covering linear program
associated with $f$. Extending the earlier results by Karzanov for
$\{0,1\}$-valued skew-supermodular functions, we present an improved polynomial
time strategy for Red to win, and give a strongly polynomial time uncrossing
procedure for dual solutions of the cut-covering LP as its consequence. We also
mention its implication on the optimality of laminar solutions.
