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We re-analyze the physical conditions for Magneto-rotational Instability(MRI) within a steady axisymmetric stratified disk of plasma, in order toaccount for the so-called isorotation theory (the spatial profile ofdifferential angular velocity depends on the magnetic flux surface). We developthe study of linear stability around an astrophysical background configuration,following the original derivation in \cite{Ba:1995}, but implementing theisorotation condition as the orthogonality between the background magneticfield and the angular velocity gradient. We demonstrate that a dependence onthe background magnetic field direction is restored in the dispersion relationand, hence, the emergence of MRI is also influenced by field orientation.

Revised Conditions for MRI due to Isorotation Theorem