  The complex Lie group GO(2n,C) by definition consists of all complex matrices
A of size 2n, such that A times transpose(A) is a non-zero scalar. In this
paper we determine explicitly the singular cohomology ring of the classifying
space BGO(2n,C) with mod 2 coefficients, in terms of generators and relations.
The method consists of analysing a certain derivation on the cohomology ring of
BO(2n) (which is a polynomial ring in the Stiefel-Whitney classes) via a Koszul
complex, and using this to `solve' the Gysin sequence for the bundle BO(2n)
over BGO(2n,C).
