Nanoscale bowtie antenna and bowtie aperture antenna have been shown to generate strongly enhanced and localized electric fields below the diffraction limit in the optical frequency range. According to Babinet's principle, their complements will be efficient for concentrating and enhancing magnetic fields. In this Letter, we discuss the enhancement of magnetic field intensity of nanoscale complementary bowtie aperture as well as complementary bowtie aperture antenna, or diabolo nanoantenna. We show that the complementary bowtie antenna resonates at a smaller wavelength and thus is more suitable for applications near visible wavelengths. The near-field magnetic intensity can be further enhanced by the addition of groove structures that scatter surface plasmon.