A square matrix pencil lambda A - B is said to be H-selfadjoint (H-uni
tary) if it satisfies AHB = B*HA (A*HA = B*HB) for some invertible He
rmitian H. Attention is focused on regular pencils (i.e., det (lambda
A B) not equivalent to 0) for which A and B are both singular. Canonic
al forms for the relation (A, B, H) similar to (Y-1 AX, Y-1 BX, YHY)
are obtained in both the complex and real cases. Also, a characterizat
ion is given for those real matrices A which are H-unitary for some H,
i.e., A(T) HA = H for some invertible, real symmetric H.