The eigenvalue equation for the interchange instability is derived from guiding-centre equations including finite-Larmor-radius corrections. Analytic solutions are found which are valid near the ⋅ = 0 surface and away from this surface. Matching these two solutions over their common range of validity determines the eigenvalue and hence the mode frequency. The growth rate and radial profile of the mode may readily be evaluated explicitly. The analysis is applicable to the high-β pinch, since cylindrical effects dominate over toroidal. For typical parameters, FLR stabilization is found to increase the marginally stable pressure gradient by a factor two over that given by the Suydam criterion.