The MiniBooNE Collaboration reports a search for νμ and ν̅ μ disappearance in the Δm2 region of 0.5–40  eV2. These measurements are important for constraining models with extra types of neutrinos, extra dimensions, and CPT violation. Fits to the shape of the νμ and ν̅ μ energy spectra reveal no evidence for disappearance at the 90% confidence level (C.L.) in either mode. The test of ν̅ μ disappearance probes a region below Δm2=40  eV2 never explored before.