  Let Q(4n,d) be the sum of all multiple zeta values of depth d and weight 4n
whose arguments are all multiples of 4. In this paper we derive a formula of
Q(4n,d) for all d>2 as a finite sum involving binomial coefficients, Bernoulli
numbers and the quantities Q(4m,2). The number of terms is about 3d^2/8 which
is independent of n.
