Multiplication of the complex numbers x and y, where \(x=a+ib\) and \(y=c+id\), requires four real multiplications, while the identity \(xy=(a(c-d)+(a-b)d)+i(b(c+d)+(a-b)d)\) requires three real multiplications instead. The author observes that this identity could be used for multiplication of complex matrices. The computational savings are shown to approach 1/4, even when a real multiplication is not more computationally costly than a real addition. Efficient algorithms for real matrix multiplication could be advantageously combined with this formula.