<p>We study a selective coaxial launder of an oversized cavity operating at the eigenmode of two higher asymmetric, spatially developed coupled modes in the context of the radiation input into a millimeter-wavelength gyroklystron. The external coaxial cavity is coupled with the internal oversized cavity and microwave sources via azimuthally periodic systems of rectangular holes in both side walls. The relation between the parameters of the coaxial launcher, which ensures the maximum transformation of the feeding-waveguide mode into the eigenmode of the internal cavity, has been found. The fundamental mode TE₁₀ of the rectangular waveguide is transformed into the eigenoscillation of the coupled TE₁₂₂₁ and TE₆₄₁ modes, which rotates azimuthally, with an efficiency of 0.6 in the absence of ohmic losses.</p>