Given a non-singular holomorphic foliation ℱ on a compact manifold M we analyze the relationship between the versal spaces K and K tr of deformations of ℱ as a holomorphic foliation and as a transversely holomorphic foliation respectively. With this purpose, we prove the existence of a versal unfolding of ℱ parametrized by an analytic space K f isomorphic to π - 1 ( 0 ) × Σ where Σ is smooth and π : K → K tr is the forgetful map. The map π is shown to be an epimorphism in two situations: (i) if H 2 ( M , Θ ℱ f ) = 0 , where Θ ℱ f is the sheaf of germs of holomorphic vector fields tangent to ℱ , and (ii) if there exists a holomorphic foliation ℱ ⋔ transverse and supplementary to ℱ . When the conditions (i) and (ii) are both fulfilled then K ≅ K f × K tr .