During the last five decades, many different secondary constructions of bent functions were proposed in the literature. Nevertheless, apart from a few works, the question about the class inclusion of bent functions generated using these methods is rarely addressed. Especially, if such a “new” family belongs to the completed Maiorana–McFarland ({{{mathcal {M}}}{{mathcal {M}}}}^#) class then there is no proper contribution to the theory of bent functions. In this article, we provide some fundamental results related to the inclusion in {{{mathcal {M}}}{{mathcal {M}}}}^# and eventually we obtain many infinite families of bent functions that are provably outside {{{mathcal {M}}}{{mathcal {M}}}}^#. The fact that a bent function f is in/outside {{{mathcal {M}}}{{mathcal {M}}}}^# if and only if its dual is in/outside {{{mathcal {M}}}{{mathcal {M}}}}^# is employed in the so-called 4-decomposition of a bent function on {mathbb {F}}_2^n, which was originally considered by Canteaut and Charpin (IEEE Trans Inf Theory 49(8):2004–2019, 2003) in terms of the second-order derivatives and later reformulated in (Hodžić et al. in IEEE Trans Inf Theory 65(11):7554–7565, 2019) in terms of the duals of its restrictions to the cosets of an (n-2)-dimensional subspace V. For each of the three possible cases of this 4-decomposition of a bent function (all four restrictions being bent, semi-bent, or 5-valued spectra functions), we provide generic methods for designing bent functions provably outside {{{mathcal {M}}}{{mathcal {M}}}}^#. For instance, for the elementary case of defining a bent function h(textbf{x},y_1,y_2)=f(textbf{x}) oplus y_1y_2 on {mathbb {F}}_2^{n+2} using a bent function f on {mathbb {F}}_2^n, we show that h is outside {{{mathcal {M}}}{{mathcal {M}}}}^# if and only if f is outside {{{mathcal {M}}}{{mathcal {M}}}}^#. This approach is then generalized to the case when two bent functions are used. More precisely, the concatenation f_1||f_1||f_2||(1oplus f_2) also gives bent functions outside {{{mathcal {M}}}{{mathcal {M}}}}^# if f_1 or f_2 is outside {{{mathcal {M}}}{{mathcal {M}}}}^#. The cases when the four restrictions of a bent function are semi-bent or 5-valued spectra functions are also considered and several design methods of constructing infinite families of bent functions outside {{{mathcal {M}}}{{mathcal {M}}}}^# are provided.