  We consider a tight-binding model defined by a matrix Hamiltonian over 2D
Brillouin zone. Multiband energy spectrum gives rise to a non-Abelian gauge
structure set by the Berry connections. The corresponding curvature
$F_{\mu\nu}$ vanishes throughout the Brillouin zone except an isolated points
where $F_{\mu\nu}$ is singular. Combining the singular behaviour of
$F_{\mu\nu}$ with non-Abelian Stokes theorem allows to avoid the path ordering
procedure in studying the structure of Wilson loops. 2D models with 2-band and
4-band energy spectra are considered as a demonstrative examples and the group
structure of the corresponding Wilson loops is revealed.
