This paper analyzes the linear stability of a rapidly-rotating, stratified sheet pinch in a gravitational field, g, perpendicular to the sheet. The sheet pinch is a layer (O ⩽ z ⩽ d) of inviscid, Boussinesq fluid of electrical conductivity σ, magnetic permeability μ, and almost uniform densityρo; z is height. The prevailing magnetic field.Bo(z), is horizontal at each z level, but varies in direction with z. The angular velocity,Ω, is vertical and large (Ω ≫ VA/d, where VA= B0√(μρ0) is the Alfvén velocity). The Elsasser number, Λ = σB20/2Ωρ0, measures σ. A (modified) Rayleigh number, R = gβd2/ρ0V2A, measures the buoyancy force, where β is the imposed density gradient, antiparallel tog. A Prandtl number, PK= μσK, measures the diffusivity, k, of density differences.