  In this paper we give the classification of standard compact Clifford-Klein
forms corresponding to triples (g,h,l) such that g = h+l and g is a sum of two
absolutely simple ideals. The classification is done using Onishchik's results
concerning semisimple decompositions of semisimple Lie algebras. Using this
classification we obtain new examples of reductive homogeneous spaces admitting
non-standard compact Clifford-Klein forms.
