In the present paper the splitting of sectoral () helioseismic eigenmodes (f- and p-modes) is studied in the presence of a magnetic atmosphere. The solar interior is in a steady state, with sub-photospheric plasma flow along the equator representing solar rotation. The Cartesian geometry employed restricts the present study to sectoral modes, . We work with , which guarantees that the modes do not deeply penetrate into the solar interior and therefore experience an approximately uniform rotation. Potentially observable effects are predicted and developments of the model to aid detections are discussed.