       ),
               (  0     C2out' )            ( -I  0  )

  and Aout, Bout, C1out are upper triangular, C2out is upper quasi-
  triangular and Dout and Fout are skew-symmetric.

  Then, orthogonal matrices Q3 and Q4 are found, for the extended
  matrices

         (  Aout   0  )          (    0   C1out )
    Se = (            ) and He = (              ),
         (   0   Bout )          ( -C2out   0   )

  such that S11 := Q4' Se Q3 is upper triangular and
  H11 := Q4' He Q3 is upper quasi-triangula