diff --git a/pyscf/fci/direct_spin1_symm.py b/pyscf/fci/direct_spin1_symm.py
index 981e170f42..3b9a6528bb 100644
--- a/pyscf/fci/direct_spin1_symm.py
+++ b/pyscf/fci/direct_spin1_symm.py
@@ -519,19 +519,34 @@ def _guess_wfnsym_cyl_sym(civec, strsa, strsb, orbsym):
     if wfn_momentum == 0:
         # For A1g and A1u, CI coefficient and its sigma_v associated one have
         # the same sign
-        if (sign_a*sign_b * c_max[0,0].real * c_max[1,1].real > 1e-6 or
-            sign_a*sign_b * c_max[0,0].imag * c_max[1,1].imag > 1e-6):  # A1
+        if (sign_a*sign_b * c_max[0,0].real * c_max[1,1].real > 1e-4 or
+            sign_a*sign_b * c_max[0,0].imag * c_max[1,1].imag > 1e-4):  # A1
             if wfn_ungerade:
                 wfnsym = 5
             else:
                 wfnsym = 0
-        else:
+        elif (sign_a*sign_b * c_max[0,0].real * c_max[1,1].real < -1e-4 or
+              sign_a*sign_b * c_max[0,0].imag * c_max[1,1].imag < -1e-4):  # A2
             # For A2g and A2u, CI coefficient and its sigma_v associated one
             # have opposite signs
             if wfn_ungerade:
                 wfnsym = 4
             else:
                 wfnsym = 1
+        elif abs(c_max[0,1] - c_max[1,0]) < 1e-4: # Off-diagonal terms only
+            # (E+)(E-') + (E-)(E+') => A1
+            if wfn_ungerade:
+                wfnsym = 5
+            else:
+                wfnsym = 0
+        elif abs(c_max[0,1] + c_max[1,0]) < 1e-4:
+            # (E+)(E-') - (E-)(E+') => A2
+            if wfn_ungerade:
+                wfnsym = 4
+            else:
+                wfnsym = 1
+        else:
+            raise RuntimeError('Symmetry broken wavefunction')
 
     elif wfn_momentum % 2 == 1:
         if abs(c_max[idx_a,idx_b].real) > 1e-6:  # Ex
diff --git a/pyscf/fci/test/test_spin1_symm.py b/pyscf/fci/test/test_spin1_symm.py
index 58a055e9be..29e44f965b 100644
--- a/pyscf/fci/test/test_spin1_symm.py
+++ b/pyscf/fci/test/test_spin1_symm.py
@@ -13,6 +13,7 @@
 # See the License for the specific language governing permissions and
 # limitations under the License.
 
+import math
 import unittest
 import numpy
 from pyscf import gto, lib
@@ -222,6 +223,19 @@ def test_many_roots(self):
                                davidson_only=True, orbsym=orbsym)
         self.assertAlmostEqual(e[0], -1.8, 9)
 
+    def test_guess_wfnsym_cyl_sym(self):
+        mol = gto.M(atom='C 0 0 0; C 0 0 1.5', basis='6-31g', symmetry=True)
+        mf = mol.RHF().run()
+        mc = mcscf.CASCI(mf, 8, 4)
+        mc.fcisolver.wfnsym = 'A1g'
+        ncas = {'A1g':2, 'A1u':2, 'E1gx':1, 'E1gy':1, 'E1ux':1, 'E1uy':1}
+        mo = mcscf.sort_mo_by_irrep(mc, mf.mo_coeff, ncas)
+        na = math.comb(8, 2)
+        ci0 = numpy.zeros((na, na))
+        ci0[1,1] = ci0[2,2] = .5**.5 # corresponding to (E+)(E-') + (E-)(E+') => A1
+        mc.kernel(mo, ci0=ci0)
+        self.assertAlmostEqual(mc.e_cas, -4.205889578214524, 9)
+
 if __name__ == "__main__":
     print("Full Tests for spin1-symm")
     unittest.main()