Metal-insulator-metal metamaterial thermal emitters or absorbers have been widely investigated, and the fundamental and higher-order modes are generally excited in these metamaterial resonators. In this paper, we propose a methodology to widen the frequency interval between the fundamental and the second-order modes by enhancing coupling between resonators in close-proximity. At the second-order mode, antiparallel magnetic fields are excited in the insulating layer of rectangular resonators. A diagonal arrangement of rectangles allows destructive interaction between neighboring resonators, resulting in higher second-order frequency. The maximum frequency interval between the two modes is achieved when resonators are shifted by half a period. Furthermore, we suggest a possibility to split the second-order mode by adjusting the arrangement of rectangles. Measured reflection spectra of fabricated metamaterial absorbers agree well with numerical simulations.