  We are reporting on the ongoing effort of the Monte Carlo (MC) modelling of
NLO DGLAP QCD evolution in the fully unintegrated form. The resulting parton
shower MC is performing on its own the NLO QCD evolution, contrary to all known
programs of this kind which are limited to LO level only. We overview this new
MC scheme, for the non-singlet subset of the gluonstrahlung diagrams. Precision
numerical tests of this new scheme are also shown.
