  In this note, starting with a little-known result of Kuo, I derive a
recurrence relation for the Bernoulli numbers $B_{2 n}$, $n$ being any positive
integer. This new recurrence seems advantageous in comparison to other known
formulae since it allows the computation of both $B_{4 n}$ and $B_{4 n +2}$
from only $B_0, B_2,..., B_{2n}$.
