  A {\em signed magic rectangle} $SMR(m,n;k, s)$ is an $m \times n$ array with
entries from $X$, where $X=\{0,\pm1,\pm2,\ldots, $ $\pm (mk-1)/2\}$ if $mk$ is
odd and $X = \{\pm1,\pm2,\ldots,\pm mk/2\}$ if $mk$ is even, such that
precisely $k$ cells in every row and $s$ cells in every column are filled,
every integer from set $X$ appears exactly once in the array and the sum of
each row and of each column is zero. In this paper, we prove that a signed
magic rectangle $SMR(m,n;k, 3)$ exists if and only if $3\leq m,k\leq n$ and
$mk=3n$.
