  To investigate the non-Fermi liquid behavior we consider the extended
two-dimensional t-J model which includes additional hopping t''. In the regime
t,J << t'' we were able to solve the model analytically. It has a very rich
phase diagram including antiferromagnetic (AF) insulator and AF strange metal
with different kinds of pseudospin-singlet superconducting pairings
(p,d,g-waves). We also demonstrate a collective triplet excitation with energy
below the superconducting gap
