We prove that the homogenization in Calculus of Variations of the functional represented by the integrand f (x, xi) = a(x) \xi\(4), where xi epsilon R(2) and a is a measurable periodic and positive real valued function on R(2), has an integrand f(infinity):R(2) --> R which is not a polynomial. This result turns out to be a counter-example to analyticity of the Gamma-limit of a sequence of functionals with analytic integrand.