--- a/liboctave/CMatrix.cc
+++ b/liboctave/CMatrix.cc
@@ -3784,20 +3784,19 @@
 // the general GEMM operation
 
 ComplexMatrix
-xgemm (bool transa, bool conja, const ComplexMatrix& a, 
-       bool transb, bool conjb, const ComplexMatrix& b)
+xgemm (const ComplexMatrix& a, const ComplexMatrix& b, 
+       blas_trans_type transa, blas_trans_type transb)
 {
   ComplexMatrix retval;
 
-  // conjugacy is ignored if no transpose
-  conja = conja && transa;
-  conjb = conjb && transb;
-
-  octave_idx_type a_nr = transa ? a.cols () : a.rows ();
-  octave_idx_type a_nc = transa ? a.rows () : a.cols ();
-
-  octave_idx_type b_nr = transb ? b.cols () : b.rows ();
-  octave_idx_type b_nc = transb ? b.rows () : b.cols ();
+  bool tra = transa != blas_no_trans, trb = transb != blas_no_trans;
+  bool cja = transa == blas_conj_trans, cjb = transb == blas_conj_trans;
+
+  octave_idx_type a_nr = tra ? a.cols () : a.rows ();
+  octave_idx_type a_nc = tra ? a.rows () : a.cols ();
+
+  octave_idx_type b_nr = trb ? b.cols () : b.rows ();
+  octave_idx_type b_nc = trb ? b.rows () : b.cols ();
 
   if (a_nc != b_nr)
     gripe_nonconformant ("operator *", a_nr, a_nc, b_nr, b_nc);
@@ -3805,18 +3804,18 @@
     {
       if (a_nr == 0 || a_nc == 0 || b_nc == 0)
 	retval = ComplexMatrix (a_nr, b_nc, 0.0);
-      else if (a.data () == b.data () && a_nr == b_nc && transa != transb)
+      else if (a.data () == b.data () && a_nr == b_nc && tra != trb)
         {
 	  octave_idx_type lda = a.rows ();
 
           retval = ComplexMatrix (a_nr, b_nc);
 	  Complex *c = retval.fortran_vec ();
 
-          const char *ctransa = get_blas_trans_arg (transa, conja);
-          if (conja || conjb)
+          const char *ctra = get_blas_trans_arg (tra, cja);
+          if (cja || cjb)
             {
               F77_XFCN (zherk, ZHERK, (F77_CONST_CHAR_ARG2 ("U", 1),
-                                       F77_CONST_CHAR_ARG2 (ctransa, 1),
+                                       F77_CONST_CHAR_ARG2 (ctra, 1),
                                        a_nr, a_nc, 1.0,
                                        a.data (), lda, 0.0, c, a_nr
                                        F77_CHAR_ARG_LEN (1)
@@ -3828,7 +3827,7 @@
           else
             {
               F77_XFCN (zsyrk, ZSYRK, (F77_CONST_CHAR_ARG2 ("U", 1),
-                                       F77_CONST_CHAR_ARG2 (ctransa, 1),
+                                       F77_CONST_CHAR_ARG2 (ctra, 1),
                                        a_nr, a_nc, 1.0,
                                        a.data (), lda, 0.0, c, a_nr
                                        F77_CHAR_ARG_LEN (1)
@@ -3850,38 +3849,38 @@
 
 	  if (b_nc == 1 && a_nr == 1)
 	    {
-              if (conja == conjb)
+              if (cja == cjb)
                 {
                   F77_FUNC (xzdotu, XZDOTU) (a_nc, a.data (), 1, b.data (), 1, *c);
-                  if (conja) *c = std::conj (*c);
+                  if (cja) *c = std::conj (*c);
                 }
-              else if (conja)
+              else if (cja)
                   F77_FUNC (xzdotc, XZDOTC) (a_nc, a.data (), 1, b.data (), 1, *c);
               else
                   F77_FUNC (xzdotc, XZDOTC) (a_nc, b.data (), 1, a.data (), 1, *c);
             }
-          else if (b_nc == 1 && ! conjb)
+          else if (b_nc == 1 && ! cjb)
             {
-              const char *ctransa = get_blas_trans_arg (transa, conja);
-              F77_XFCN (zgemv, ZGEMV, (F77_CONST_CHAR_ARG2 (ctransa, 1),
+              const char *ctra = get_blas_trans_arg (tra, cja);
+              F77_XFCN (zgemv, ZGEMV, (F77_CONST_CHAR_ARG2 (ctra, 1),
                                        lda, tda, 1.0,  a.data (), lda,
                                        b.data (), 1, 0.0, c, 1
                                        F77_CHAR_ARG_LEN (1)));
             }
-          else if (a_nr == 1 && ! conja && ! conjb)
+          else if (a_nr == 1 && ! cja && ! cjb)
             {
-              const char *crevtransb = get_blas_trans_arg (! transb, conjb);
-              F77_XFCN (zgemv, ZGEMV, (F77_CONST_CHAR_ARG2 (crevtransb, 1),
+              const char *crevtrb = get_blas_trans_arg (! trb, cjb);
+              F77_XFCN (zgemv, ZGEMV, (F77_CONST_CHAR_ARG2 (crevtrb, 1),
                                        ldb, tdb, 1.0,  b.data (), ldb,
                                        a.data (), 1, 0.0, c, 1
                                        F77_CHAR_ARG_LEN (1)));
             }
 	  else
 	    {
-              const char *ctransa = get_blas_trans_arg (transa, conja);
-              const char *ctransb = get_blas_trans_arg (transb, conjb);
-	      F77_XFCN (zgemm, ZGEMM, (F77_CONST_CHAR_ARG2 (ctransa, 1),
-				       F77_CONST_CHAR_ARG2 (ctransb, 1),
+              const char *ctra = get_blas_trans_arg (tra, cja);
+              const char *ctrb = get_blas_trans_arg (trb, cjb);
+	      F77_XFCN (zgemm, ZGEMM, (F77_CONST_CHAR_ARG2 (ctra, 1),
+				       F77_CONST_CHAR_ARG2 (ctrb, 1),
 				       a_nr, b_nc, a_nc, 1.0, a.data (),
 				       lda, b.data (), ldb, 0.0, c, a_nr
 				       F77_CHAR_ARG_LEN (1)
@@ -3896,7 +3895,7 @@
 ComplexMatrix
 operator * (const ComplexMatrix& a, const ComplexMatrix& b)
 {
-  return xgemm (false, false, a, false, false, b);
+  return xgemm (a, b);
 }
 
 // FIXME -- it would be nice to share code among the min/max