diff --git a/nbconvert/exporters/exporter.py b/nbconvert/exporters/exporter.py
index 9c7abcc8e..396e30175 100644
--- a/nbconvert/exporters/exporter.py
+++ b/nbconvert/exporters/exporter.py
@@ -315,10 +315,7 @@ def _init_resources(self, resources):
 
     def _validate_preprocessor(self, nbc, preprocessor):
         try:
-            if not hasattr(validator, "normalize"):
-                nbformat.validate(nbc, relax_add_props=True)
-            else:
-                nbformat.validate(nbc)
+            nbformat.validate(nbc, relax_add_props=True)
         except nbformat.ValidationError:
             self.log.error("Notebook is invalid after preprocessor %s", preprocessor)
             raise
diff --git a/pyproject.toml b/pyproject.toml
index 4e00a11ed..f775c8685 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -153,8 +153,6 @@ testpaths = [
 filterwarnings = [
     "error",
     "ignore:nbconvert.utils.lexers is deprecated as of 5.0:UserWarning",
-    # Pending https://github.com/jupyter/nbformat/pull/256
-    "ignore:Passing a schema to Validator.iter_errors is deprecated:DeprecationWarning",
     # https://github.com/pyppeteer/pyppeteer/issues/342
     "ignore:remove loop argument:DeprecationWarning:websockets",
     # https://github.com/mhammond/pywin32/issues/1802