We prove that given a smooth function f:Rⁿ → R and a submanifold M ⊂ Rⁿ, then the set of a=(a₁,..., a_n) ∈ Rⁿ such that (f+q_a)|_M is Morse, where q_a(x)=a₁x₁²+... +a_nx_n², is residual in Rⁿ. The classical literature covers perturbations by linear functions and quadratic ones but doesn't give an answer to the case of sums of squares: in fact standard transversality arguments do not work and we need a more refined approach.