  Belokurov-Usyukina loop reduction method has been proposed in 1983 to reduce
a number of rungs in triangle ladder-like diagram by one. The disadvantage of
the method is that it works in d=4 dimensions only and it cannot be used for
calculation of amplitudes in field theory in which we are required to put all
the incoming and outgoing momenta on shell. We generalize the
Belokurov-Usyukina loop reduction technique to non-integer d=4-2e dimensions.
In this paper we show how a two-loop triangle diagram with particular values of
indices of scalar propagators in the position space can be reduced to a
combination of three one-loop scalar diagrams. It is known that any one-loop
massless momentum integral can be presented in terms of Appell's function F_4.
This means that particular diagram considered in the present paper can be
represented in terms of Appell's function F_4 too. Such a generalization of
Belokurov-Usyukina loop reduction technique allows us to calculate that diagram
by this method exactly without decomposition in terms of the parameter e.
