Let R be a ring with 2 ∈ R × . Then the usual Vaserstein symbol is a map from the orbit space of unimodular rows of length 3 under the action of the group E3(R) to the elementary symplectic Witt group. Now let P0 be a projective module of rank 2 with trivial determinant. Then we provide a generalized symbol map which is defined on the orbit space of the set of epimorphisms P0 ⊕ R → R under the action of the group of elementary automorphisms of P0 ⊕ R. We also generalize results by Vaserstein and Suslin on the surjectivity and injectivity of the Vaserstein symbol. Finally, we use local-global principles for transvection groups in order to deduce that the generalized Vaserstein symbol is an isomorphism if R is a regular Noetherian ring of dimension 2 or a regular affine algebra of dimension 3 over a field k with c.d.(k) ≤ 1 and 6 ∈ k × .

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