  We find the exotic matrix bialgebras which correspond to the two
non-triangular nonsingular 4x4 R-matrices in the classification of Hietarinta,
namely, R_{S0,3} and R_{S1,4}. We find two new exotic bialgebras S03 and S14
which are not deformations of the of the classical algebras of functions on
GL(2) or GL(1|1). With this we finalize the classification of the matrix
bialgebras which unital associative algebras generated by four elements. We
also find the corresponding dual bialgebras of these new exotic bialgebras and
study their representation theory in detail. We also discuss in detail a
special case of R_{S1,4} in which the corresponding algebra turns out to be a
special case of the two-parameter quantum group deformation GL_{p,q}(2).
