An \(m \times n\) magic rectangle is an \(m \times n\) array of the integers \(1, 2, \ldots, mn\) so that the sum of the entries is constant in each row (\( \frac n{mn+1,2}\)) and in each column (\(\frac m{mn+1,2}\)). The necessary conditions (\(m, n >1\), \((m,n) \neq (2,2)\) and \(m\) and \(n\) of the same parity) have long been known to be sufficient. The author provides a simple proof.