  The quasi-local notion of an isolated horizon is employed to study the
entropy of black holes without any particular symmetry in loop quantum gravity.
The idea of characterizing the shape of a horizon by a sequence of local areas
is successfully applied in the scheme to calculate the entropy by the $SO(1,1)$
BF boundary theory matching loop quantum gravity in the bulk. The generating
function for calculating the microscopical degrees of freedom of a given
isolated horizon is obtained. Numerical computations of small black holes
indicate a new entropy formula containing the quantum correction related to the
partition of the horizon. Further evidence shows that, for a given horizon
area, the entropy decreases as a black hole deviates from the spherically
symmetric one, and the entropy formula is also well suitable for big black
holes.
