  We give a basis of bideterminants for the coordinate ring K[O(n)] of the
orthogonal group O(n,K), where K is an infinite field of characteristic not 2.
The bideterminants are indexed by pairs of Young tableaux which are
O(n)-standard in the sense of King-Welsh. We also give an explicit filtration
of K[O(n)] as an O(n,K)-bimodule, whose factors are isormorphic to the tensor
product of orthogonal analogues of left and right Schur modules.
