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We propose, for the first time, a tunable left-handed (LH) waveguide consisting of an array of complementary split-ring resonators built on the broad wall of a rectangular waveguide filled with ferrite material. The left-handed behavior is caused by the negative permittivity of the complementary split-ring resonators together with the negative permeability of the transversely magnetized ferrite. The electromagnetic behavior of this structure is studied by means of an equivalent circuit model. From this model, the dispersion relation of the guide is derived and validated numerically by the finite element method. It is shown that this structure has a left-handed frequency band that can be tuned by changing the dc bias magnetic field applied to the ferrite. Compared to previous works, the fabrication requirements on this structure are not critical, which enhances its potential applicability.