  This article is a follow-up of ``Holonomy and Path Structures in General
Relativity and Yang-Mills Theory" by Barrett, J. W. (Int.J.Theor.Phys., vol.30,
No.9, 1991). Its main goal is to provide an alternative proof of this part of
the reconstruction theorem which concerns the existence of a connection. A
construction of connection 1-form is presented. The formula expressing the
local coefficients of connection in terms of the holonomy map is obtained as an
immediate consequence of that construction. Thus the derived formula coincides
with that used in "On Loop Space Formulation of Gauge Theories" by Chan, H.-M.,
Scharbach, P. and Tsou S.T. (Ann.Phys., vol.167, 454-472, 1986). The
reconstruction and representation theorems form a generalization of the fact
that the pointed configuration space of the classical Yang-Mills theory is
equivalent to the set of all holonomy maps. The point of this generalization is
that there is a one-to-one correspondence not only between the holonomy maps
and the orbits in the space of connections, but also between all maps from the
loop space on $M$ to group $G$ fulfilling some axioms and all possible
equivalence classes of $P(M,G)$ bundles with connection, where the equivalence
relation is defined by bundle isomorphism in a natural way.
