Let v be a function defined on an open set Ω of RN . It satisfies the Neumann condition ∂v/∂n = g on the boundary Γ of Ω. The first variation v' of v under the variation of Ω is investigated. The variation of Ω is represented by tθ where θ is a vector field and t is a real number. Whenever v(Ω+tθ) depends “smoothly” on t it is proved that its derivative at t=0, v' = ∂v(Ω+tΩ)/∂t satisfies a Neumann condition on Γ. It is ∂v'/∂n = Ω.n(∂g/∂n - ∂2v/∂n2) + grad v.gradΓθ.n on Γ. The normal component θ.n of θ is defined on Γ and gradΓθ.n is its derivative along the boundary. This is a “Hadamard formula”. It relies on the differentiation of an extension of n and of the boundary condition u.n=g on Γ for a vector valued function u. An application to an optimal design problem involving Neumann condition is considered.