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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 ($${{{\mathcal {M}}}{{\mathcal {M}}}}^\#$$ M 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 $${{{\mathcal {M}}}{{\mathcal {M}}}}^\#$$ M M # and eventually we obtain many infinite families of bent functions that are provably outside $${{{\mathcal {M}}}{{\mathcal {M}}}}^\#$$ M M # . The fact that a bent function f is in/outside $${{{\mathcal {M}}}{{\mathcal {M}}}}^\#$$ M M # if and only if its dual is in/outside $${{{\mathcal {M}}}{{\mathcal {M}}}}^\#$$ M M # is employed in the so-called 4-decomposition of a bent function on $${\mathbb {F}}_2^n$$ 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 $$(n-2)$$ ( 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 $${{{\mathcal {M}}}{{\mathcal {M}}}}^\#$$ M M # . For instance, for the elementary case of defining a bent function $$h(\textbf{x},y_1,y_2)=f(\textbf{x}) \oplus y_1y_2$$ h ( x , y 1 , y 2 ) = f ( x ) ⊕ y 1 y 2 on $${\mathbb {F}}_2^{n+2}$$ F 2 n + 2 using a bent function f on $${\mathbb {F}}_2^n$$ F 2 n , we show that h is outside $${{{\mathcal {M}}}{{\mathcal {M}}}}^\#$$ M M # if and only if f is outside $${{{\mathcal {M}}}{{\mathcal {M}}}}^\#$$ M M # . This approach is then generalized to the case when two bent functions are used. More precisely, the concatenation $$f_1||f_1||f_2||(1\oplus f_2)$$ f 1 | | f 1 | | f 2 | | ( 1 ⊕ f 2 ) also gives bent functions outside $${{{\mathcal {M}}}{{\mathcal {M}}}}^\#$$ M M # if $$f_1$$ f 1 or $$f_2$$ f 2 is outside $${{{\mathcal {M}}}{{\mathcal {M}}}}^\#$$ M 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 $${{{\mathcal {M}}}{{\mathcal {M}}}}^\#$$ M M # are provided.