  We establish a congruence modulo four in the real Schubert calculus on the
Grassmannian of m-planes in 2m-space. This congruence holds for fibers of the
Wronski map and a generalization to what we call symmetric Schubert problems.
This strengthens the usual congruence modulo two for numbers of real solutions
to geometric problems. It also gives examples of geometric problems given by
fibers of a map whose topological degree is zero but where each fiber contains
real points.
