  With the imminent start of LHC experiments, development of phenomenological
tools, and in particular the Monte Carlo programs and algorithms, becomes
urgent. A new algorithm for the generation of a parton shower initiated by the
single initial hadron beam is presented. The new algorithm is of the class of
the so called ``constrained MC'' type algorithm (an alternative to the backward
evolution MC algorithm), in which the energy and the type of the parton at the
end of the parton shower are constrained (predefined). The complete kinematics
configurations with explicitly constructed four momenta are generated and
tested. Evolution time is identical with rapidity and minimum transverse
momentum is used as an infrared cut-off. All terms of the leading-logarithmic
approximation in the DGLAP evolution are properly accounted for. In addition,
the essential improvements towards the so-called CCFM/BFKL models are also
properly implemented. The resulting parton distributions are cross-checked up
to the 0.1% precision level with the help of a multitude of comparisons with
other MC and non-MC programs. We regard these tests as an important asset to be
exploited at the time when the presented MC will enter as a building block in a
larger MC program for W/Z production process at LHC.
