In 1962 Steinberg gave pairs of generators for all finite simple group
s of Lie type. In this paper, for each finite orthogonal group we prov
ide a pair of matrices which generate its derived group: the matrices
correspond to Steinberg's generators module the centre. These generato
rs have been implemented in the computer algebra system MAGMA and this
completes the provision of pairs of generators in MAGMA for all (perf
ect) finite classical groups. (C) 1998 Academic Press Limited.