  In this paper, we prove that given a 2-edge-coloured complete graph $K_{4n}$
that has the same number of edges of each colour, we can always find a perfect
matching with an equal number of edges of each colour. This solves a problem
posed by Caro, Hansberg, Lauri, and Zarb. The problem is also independently
solved by Ehard, Mohr, and Rautenbach.
