  We discuss the relationship between the quantum Hall conductance and a
fractal energy band structure, Hofstadter's butterfly, on a square lattice
under a magnetic field. At first, we calculate the Hall conductance of
Hofstadter's butterfly on the basis of the linear responce theory. By
classifying the bands into some groups with a help of continued fraction
expansion, we find that the conductance at the band gaps between the groups
accord with the denominators of fractions obtained by aborting the expansion
halfway. The broadening of Landau levels is given as an account of this
correspondance.
