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For an odd quadratic space $V$ of Witt index $\geq 3$ over a commutative ringwith pseudoinvolution, we classify the subgroups of the odd unitary group$U(V)$ that are normalized by the elementary subgroup $EU_{(e_1,e_{-1})}(V)$defined by a hyperbolic pair $(e_1,e_{-1})$ in $V$. Further we correct someminor mistakes that exist in the literature on odd unitary groups.

The E-normal structure of Petrov's odd unitary groups over commutative rings