We　consider　the　magnetic　Bénard　problem　for　a　horizontal　layer　of　inviscid,　thermally　and　electrically　conducting　fluid,　and　prove　that　the　thermal　convection　is　inhibited　by　a　strong　enough　uniform　vertical　magnetic　field.　The　key　ingredient　here　is　to　use　a　new　representation　of　the　vertical　component　of　the　velocity,　derived　from　the　magnetic　equations　due　to　the　transversality　of　the　magnetic　field,　to　control　the　thermal　instability.　This　works　also　for　the　classical　viscous　magnetic　Bénard　problem,　which　in　particular　improves　the　result　of　Galdi　(Arch　Ration　Mech　Anal　62(2):167–186,　1985)　in　the　large　Chandrasekhar　number　limit　and　justifies,　in　the　nonlinear　sense,　the　theory　in　Chandrasekhar　(Hydrodynamic　and　Hydromagnetic　Stability.　The　International　Series　of　Monographs　on　Physics,　Clarendon　Press,　Oxford,　1961)　that　the　temperature　gradient　for　the　onset　of　convection　is　independent　of　the　viscosity　in　this　limit.　©　2022,　The　Author(s),　under　exclusive　licence　to　Springer　Nature　Switzerland　AG.