diff --git a/sqlite_utils/db.py b/sqlite_utils/db.py
index 7cc1c99..2b2091a 100644
--- a/sqlite_utils/db.py
+++ b/sqlite_utils/db.py
@@ -219,11 +219,6 @@ class AlterError(Exception):
     pass
 
 
-class FunctionAlreadyRegistered(Exception):
-    "A function with this name and arity was already registered"
-    pass
-
-
 class NoObviousTable(Exception):
     "Could not tell which table this operation refers to"
     pass
@@ -414,9 +409,7 @@ class Database:
             fn_name = name or fn.__name__
             arity = len(inspect.signature(fn).parameters)
             if not replace and (fn_name, arity) in self._registered_functions:
-                raise FunctionAlreadyRegistered(
-                    f'Already registered function with name "{fn_name}" and identical arity'
-                )
+                return fn
             kwargs = {}
             registered = False
             if deterministic:
diff --git a/tests/test_register_function.py b/tests/test_register_function.py
index 5b92631..e2591f4 100644
--- a/tests/test_register_function.py
+++ b/tests/test_register_function.py
@@ -3,7 +3,6 @@ import pytest
 import sys
 from unittest.mock import MagicMock, call
 from sqlite_utils.utils import sqlite3
-from sqlite_utils.db import FunctionAlreadyRegistered
 
 
 def test_register_function(fresh_db):
@@ -85,12 +84,10 @@ def test_register_function_replace(fresh_db):
 
     assert "one" == fresh_db.execute("select one()").fetchone()[0]
 
-    # This will fail to replace the function:
-    with pytest.raises(FunctionAlreadyRegistered):
-
-        @fresh_db.register_function()
-        def one():  # noqa
-            return "two"
+    # This will silently fail to replaec the function
+    @fresh_db.register_function()
+    def one():  # noqa
+        return "two"
 
     assert "one" == fresh_db.execute("select one()").fetchone()[0]
 
@@ -100,12 +97,3 @@ def test_register_function_replace(fresh_db):
         return "two"
 
     assert "two" == fresh_db.execute("select one()").fetchone()[0]
-
-
-def test_register_function_duplicate(fresh_db):
-    def to_lower(s):
-        return s.lower()
-
-    fresh_db.register_function(to_lower)
-    with pytest.raises(FunctionAlreadyRegistered):
-        fresh_db.register_function(to_lower)