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In applied electromagnetics Faraday's effect is usually considered and used in cases of boundless medium or regular circular waveguide filled by longitudinally magnetized ferrite. Functional possibilities of nonreciprocal microwave devices can be extended by using nonregular waveguides with rectangular cross section. In the present work we theoretically consider local coupling of transverse electric waves TE_2m+1,0 and TE_0,2n+1 propagating in rectangular waveguide formed by surfaces x and y and filled by homo-geneous longitudinally gyrotropic medium.