  An $n \times m$ non-negative matrix with row sum $m$ and column sum $n$ is
called doubly stochastic. We answer the problem of finding doubly stochastic
matrices of smallest posible support for every $1 <n \leq m$. Any matrix of
minimum support is extremal in the sence of convexity, while examples of
extremal matrices that are not of minimum support are given. But when $n,m$ are
coprime integers extremal matrices are precisely those of minimum support.
