Let A be an involution ring, e₁,.. , e_n be a full system of Hermitian idempotents in A, let every ei generate A as a two-sided ideal, and 2 ∈ A^∗. In this paper, the normalizers of the groups Ep(2,A) · E(2,A, I) are calculated under natural assumptions on A, where Ep(2,A) denotes the elementary symplectic group, E(2,A, I) stands for the elementary subgroup of level I.