Let $B_{r}$ denote the Bernoulli numbers, and $S(r,k)$ denote the Stirling numbers of the second kind. We prove the following identity$$ B_{2r} = (-1)^{r}\sum_{k=1}^{2r}\frac{(-1)^{k-1}\cdot (k-1)!}{k+1}\sum_{l=1}^{k}\frac{S(r,l)\, S(r,k-l)}{\binom{k}{l}}. $$To the best of our knowledge, the identity is new.