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This paper is focused on the study of an inverse problem for anon-self-adjoint hyperbolic equation. More precisely, we attempt to stablyrecover a first order coefficient appearing in a wave equation from theknowledge of Neumann boundary data. We show in dimension n greater than two, astability estimate of H{\"o}lder type for the inverse problem underconsideration. The proof involves the reduction to an auxiliary inverse problemfor an electromagnetic wave equation and the use of an appropriate Carlemanestimate.

Optimal stability for a first order coefficient in a non-self-adjoint wave equation from dirichlet-to-neumann map