A simple theory is developed for a flute mode with frequency between the electron and ion bounce frequencies in the uniform density and temperature regions of a magnetic quadrupole. The frequency is predicted to be inversely proportional to the wave number. Similarity between the present theoretical dispersion curve and the experimental dispersion curve for a mode recently observed in the private flux region of the UMIST quadrupole suggests that the latter may be an intermediate-frequency, uniform-plasma flute mode.