  The improved lattice regularization method of the Ashtekar connection
holonomy representation in loop quantum gravity is described in this article.
The approach is based on the geometric expansion of holonomies into power
series up to the quadratic order terms in the regularization parameter. As a
result, a more accurate procedure than the currently established approach to
the canonical lattice quantization of gravity is obtained. Moreover, in the
improved method, the symmetry of holonomies assigned to links is directly
reflected in the related distribution of connections. The application of the
procedure to the Hamiltonian constraint regularization provides its lattice
analog, the domain of which has a natural structure of elementary cells sum. In
consequence, the related scalar constraint operator, which spectrum is
independent of intertwiners, can be defined.
