Isotropic odd unitary groups generalize Chevalley groups of classical types over commutative rings and their twisted forms. Such groups have root subgroups parameterized by a root system BCℓ and may be constructed by so-called odd form rings with Peirce decompositions. We show the converse: if a group G has root subgroups indexed by roots of BCℓ and satisfying natural conditions, then there is a homomorphism [Figure presented] inducing isomorphisms on the root subgroups, where [Figure presented] is the odd unitary Steinberg group constructed by an odd form ring (R,Δ) with a Peirce decomposition. For groups with root subgroups indexed by Aℓ (the already known case) the resulting odd form ring is essentially a generalized matrix ring.