  Maker-Breaker subgraph games are among the most famous combinatorial games.
For given $n,q \in \mathbb{N}$ and a subgraph $C$ of the complete graph $K_n$,
the two players, called Maker and Breaker, alternately claim edges of $K_n$. In
each round of the game Maker claims one edge and Breaker is allowed to claim up
to $q$ edges. If Maker is able to claim all edges of a copy of $C$, he wins the
game. Otherwise Breaker wins. In this work we introduce the first constructive
strategy for Maker for the $C_4$-Maker-Breaker game and show that he can win
the game if $q < 0.16 n^{2/3}$. According to the theorem of Bednarska and
Luczak (2000) $n^{2/3}$ is asymptotically optimal for this game, but the
constant given there for a random Maker strategy is magnitudes apart from our
constant 0.16.
