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I. Introduction. The purpose of this note is to show that an analogue to Witt's theorem holds for a nondegenerate, nonalternating, symmetric bilinear form / over a field K of characteristic 2 where f(x, x) takes its values in a subfield K* such that K contains the square root of any element in K*. As is known [2, p. 171 ] Witt's theorem does not hold in general for a field of characteristic 2. However , the following shows that an isometry of a subspace can be extended if it leaves a certain unique vector invariant. The invariants of a subspace of V with respect to the orthogonal group are determined .

On Witt’s theorem for nonalternating symmetric bilinear forms over a field of characteristic $2$