diff --git a/docs/python-api.rst b/docs/python-api.rst
index 9f69b34..b008cb5 100644
--- a/docs/python-api.rst
+++ b/docs/python-api.rst
@@ -1719,3 +1719,13 @@ Python 3.8 added the ability to register `deterministic SQLite functions <https:
         return "".join(reversed(list(s)))
 
 If you run this on a version of Python prior to 3.8 your code will still work, but the ``deterministic=True`` parameter will be ignored.
+
+By default registering a function with the same name and number of arguments will have no effect - the ``Database`` instance keeps track of functions that have already been registered and skips registering them if ``@db.register_function`` is called a second time.
+
+If you want to deliberately replace the registered function with a new implementation, use the ``replace=True`` argument:
+
+.. code-block:: python
+
+    @db.register_function(deterministic=True, replace=True)
+    def reverse_string(s):
+        return s[::-1]
diff --git a/setup.py b/setup.py
index 304f69c..9e1aea9 100644
--- a/setup.py
+++ b/setup.py
@@ -22,7 +22,7 @@ setup(
     version=VERSION,
     license="Apache License, Version 2.0",
     packages=find_packages(exclude=["tests", "tests.*"]),
-    install_requires=["click", "click-default-group", "tabulate"],
+    install_requires=["sqlite-fts4", "click", "click-default-group", "tabulate"],
     setup_requires=["pytest-runner"],
     extras_require={
         "test": ["pytest", "black", "hypothesis"],
diff --git a/sqlite_utils/db.py b/sqlite_utils/db.py
index bfbd17c..6a41932 100644
--- a/sqlite_utils/db.py
+++ b/sqlite_utils/db.py
@@ -154,6 +154,7 @@ class Database:
         self._tracer = tracer
         if recursive_triggers:
             self.execute("PRAGMA recursive_triggers=on;")
+        self._registered_functions = set()
 
     @contextlib.contextmanager
     def tracer(self, tracer=None):
@@ -170,14 +171,17 @@ class Database:
     def __repr__(self):
         return "<Database {}>".format(self.conn)
 
-    def register_function(self, fn=None, deterministic=None):
+    def register_function(self, fn=None, deterministic=None, replace=False):
         def register(fn):
             name = fn.__name__
             arity = len(inspect.signature(fn).parameters)
+            if not replace and (name, arity) in self._registered_functions:
+                return fn
             kwargs = {}
             if deterministic and sys.version_info >= (3, 8):
                 kwargs["deterministic"] = True
             self.conn.create_function(name, arity, fn, **kwargs)
+            self._registered_functions.add((name, arity))
             return fn
 
         if fn is None:
diff --git a/tests/test_register_function.py b/tests/test_register_function.py
index dab0a8d..e6d977a 100644
--- a/tests/test_register_function.py
+++ b/tests/test_register_function.py
@@ -44,3 +44,25 @@ def test_register_function_deterministic_registered(fresh_db):
     fresh_db.conn.create_function.assert_called_with(
         "to_lower_2", 1, to_lower_2, deterministic=True
     )
+
+
+def test_register_function_replace(fresh_db):
+    @fresh_db.register_function()
+    def one():
+        return "one"
+
+    assert "one" == fresh_db.execute("select one()").fetchone()[0]
+
+    # This will fail to replace the function:
+    @fresh_db.register_function()
+    def one():
+        return "two"
+
+    assert "one" == fresh_db.execute("select one()").fetchone()[0]
+
+    # This will replace it
+    @fresh_db.register_function(replace=True)
+    def one():
+        return "two"
+
+    assert "two" == fresh_db.execute("select one()").fetchone()[0]