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In fact, any matrix $X$ can be written as $X=\lambda(U+V)$ for unitary matrices $U,V$, and $\lambda$ can be taken as a half of the operator norm of $X$. For a proof, see this question. This is slightly stronger than Matthew's comment, and the proof works in any von Neumann algebra. In a $C^*$-algebra this is not possible (consider $z \mapsto z$ in the $C^*$-algebra of continuous functions on the unit disc of the complex plane) but, as noted by Matthew, you can get the same decomposition with $4$ unitaries.