diff --git a/src/aiida_quantumespresso_hp/workflows/hubbard.py b/src/aiida_quantumespresso_hp/workflows/hubbard.py
index 529c982..ab6f9ff 100644
--- a/src/aiida_quantumespresso_hp/workflows/hubbard.py
+++ b/src/aiida_quantumespresso_hp/workflows/hubbard.py
@@ -615,6 +615,8 @@ def inspect_hp(self):
 
     def check_convergence(self):
         """Check the convergence of the Hubbard parameters."""
+        from aiida_quantumespresso.utils.hubbard import is_intersite_hubbard
+
         workchain = self.ctx.workchains_hp[-1]
 
         # We store in memory the parameters before relabelling to make the comparison easier.
@@ -631,16 +633,17 @@ def check_convergence(self):
         # We check if new types were created, in which case we relabel the `HubbardStructureData`
         self.ctx.current_hubbard_structure = workchain.outputs.hubbard_structure
 
-        for site in workchain.outputs.hubbard.dict.sites:
-            if not site['type'] == site['new_type']:
-                self.report('new types have been detected: relabeling the structure and starting new iteration.')
-                result = structure_relabel_kinds(
-                    self.ctx.current_hubbard_structure, workchain.outputs.hubbard, self.ctx.current_magnetic_moments
-                )
-                self.ctx.current_hubbard_structure = result['hubbard_structure']
-                if self.ctx.current_magnetic_moments is not None:
-                    self.ctx.current_magnetic_moments = result['starting_magnetization']
-                break
+        if not is_intersite_hubbard(workchain.outputs.hubbard_structure.hubbard):
+            for site in workchain.outputs.hubbard.dict.sites:
+                if not site['type'] == site['new_type']:
+                    self.report('new types have been detected: relabeling the structure and starting new iteration.')
+                    result = structure_relabel_kinds(
+                        self.ctx.current_hubbard_structure, workchain.outputs.hubbard, self.ctx.current_magnetic_moments
+                    )
+                    self.ctx.current_hubbard_structure = result['hubbard_structure']
+                    if self.ctx.current_magnetic_moments is not None:
+                        self.ctx.current_magnetic_moments = result['starting_magnetization']
+                    break
 
         if not len(ref_params) == len(new_params):
             self.report('The new and old Hubbard parameters have different lenghts. Assuming to be at the first cycle.')
diff --git a/tests/workflows/test_hubbard.py b/tests/workflows/test_hubbard.py
index 41482d4..feda8fe 100644
--- a/tests/workflows/test_hubbard.py
+++ b/tests/workflows/test_hubbard.py
@@ -329,8 +329,6 @@ def test_not_converged_check_convergence(
 
     process.setup()
 
-    # Mocking current (i.e. "old") and "new" HubbardStructureData,
-    # containing different Hubbard parameters
     process.ctx.current_hubbard_structure = generate_hubbard_structure()
     process.ctx.workchains_hp = [generate_hp_workchain_node(u_value=5.0)]
 
@@ -354,19 +352,26 @@ def test_relabel_check_convergence(
 
     process.setup()
 
-    # Mocking current (i.e. "old") and "new" HubbardStructureData,
-    # containing different Hubbard parameters
-    process.ctx.current_hubbard_structure = generate_hubbard_structure()
-    process.ctx.workchains_hp = [generate_hp_workchain_node(relabel=True, u_value=100)]
-
+    current_hubbard_structure = generate_hubbard_structure(u_value=1, only_u=True)
+    process.ctx.current_hubbard_structure = current_hubbard_structure
+    process.ctx.workchains_hp = [generate_hp_workchain_node(relabel=True, u_value=100, only_u=True)]
     process.check_convergence()
     assert not process.ctx.is_converged
+    assert process.ctx.current_hubbard_structure.get_kind_names() != current_hubbard_structure.get_kind_names()
 
-    process.ctx.current_hubbard_structure = generate_hubbard_structure(u_value=99.99)
-    process.ctx.workchains_hp = [generate_hp_workchain_node(relabel=True, u_value=100)]
+    current_hubbard_structure = generate_hubbard_structure(u_value=99.99, only_u=True)
+    process.ctx.current_hubbard_structure = current_hubbard_structure
+    process.ctx.workchains_hp = [generate_hp_workchain_node(relabel=True, u_value=100, only_u=True)]
+    process.check_convergence()
+    assert process.ctx.is_converged
+    assert process.ctx.current_hubbard_structure.get_kind_names() != current_hubbard_structure.get_kind_names()
 
+    current_hubbard_structure = generate_hubbard_structure(u_value=99.99)
+    process.ctx.current_hubbard_structure = current_hubbard_structure
+    process.ctx.workchains_hp = [generate_hp_workchain_node(relabel=True, u_value=100)]
     process.check_convergence()
     assert process.ctx.is_converged
+    assert process.ctx.current_hubbard_structure.get_kind_names() == current_hubbard_structure.get_kind_names()
 
 
 @pytest.mark.usefixtures('aiida_profile')