Let $K$ be a finite simplicial complex and let $k$ be a field. The Stanley-Reisner ring $k[K]$ is Cohen-Macaulay if and only if, for every face $\sigma\in K$ including $\sigma=\varnothing$, the reduced homology groups satisfy $\tilde H_i(\operatorname{lk}_K(\sigma);k)=0$ for all $i<\dim \operatorname{lk}_K(\sigma)$.