  We present a new conformal algebra. It is Z2 x Z2 graded and generated by
three N=1 superconformal algebras coupled to each other by nontrivial relations
of parafermionic type. The representation theory and unitary models of the
algebra are briefly discussed. We also conjecture the existence of infinite
series of parafermionic algebras containing many N=1 or N=2 superconformal
subalgebras.
