diff --git a/pyscf/tdscf/_lr_eig.py b/pyscf/tdscf/_lr_eig.py
index 41206dead..0937fed8f 100644
--- a/pyscf/tdscf/_lr_eig.py
+++ b/pyscf/tdscf/_lr_eig.py
@@ -694,7 +694,8 @@ def real_eig(aop, x0, precond, tol_residual=1e-5, nroots=1, x0sym=None, pick=Non
             break
 
         r_index = r_norms > tol_residual
-        XY_new = precond(np.vstack([R_x[:,r_index], -R_y[:,r_index]]).T, w[r_index])
+        XY_new = precond(np.vstack([R_x[:,r_index], -R_y[:,r_index]]).T,
+                         w[r_index] + 5e-2)
         X_new = XY_new[:,:A_size].T
         Y_new = XY_new[:,A_size:].T
         if x0sym is None: