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At millimeter-wave (mm-wave) frequencies, the size of the dielectric resonator antenna (DRA) may be too small to fabricate precisely. To relax the precision problem of fabrication, it is proposed to obtain a larger DRA by designing it with its higher-order mode. In this paper, the rectangular mm-wave slot-fed DRA excited in a higher-order mode is investigated systematically. It is found that when the slot is centrally located beneath the DRA, a TEpqr mode of the DRA can be excited only when all of the indices p, q, r are odd numbers. The aspect ratio of the DRA that gives a single (higher-order) TE11ry -mode operation is found. Like the fundamental TE111 mode, the higher-order TE11r modes have broadside radiation patterns. To validate our results, two DRAs were designed to operate in the higher-order TE115 and TE119 modes. In each case, the reflection coefficient, radiation pattern, and antenna gain are studied, and reasonable agreement between the measured and simulated results is observed. The effect of fabrication error on the frequency shift of the DRA was also studied. A design rule for minimizing the frequency shift is suggested. The results should be useful for practical designs of the mm-wave DRA.