diff --git a/.cirrus.yml b/.cirrus.yml
index b3992de64a..efe7881548 100644
--- a/.cirrus.yml
+++ b/.cirrus.yml
@@ -32,7 +32,7 @@ env:
   # Increment the build number to force new nox cache upload.
   NOX_CACHE_BUILD: "0"
   # Increment the build number to force new pip cache upload.
-  PIP_CACHE_BUILD: "0"
+  PIP_CACHE_BUILD: "1"
   # Pip packages to be upgraded/installed.
   PIP_CACHE_PACKAGES: "nox pip pyyaml setuptools wheel"
   # Conda packages to be installed.
diff --git a/docs/src/whatsnew/latest.rst b/docs/src/whatsnew/latest.rst
index 33f2e7a699..44ad6c0fcd 100644
--- a/docs/src/whatsnew/latest.rst
+++ b/docs/src/whatsnew/latest.rst
@@ -202,10 +202,16 @@ This document explains the changes made to Iris for this release
 #. `@rcomer`_ modified a NetCDF saver test to prevent it triggering a numpy
    deprecation warning.  (:issue:`4374`, :pull:`4376`)
 
+#. `@akuhnregnier`_ removed addition of period from
+   :func:`~iris.analysis.cartography.wrap_lons` and updated affected tests
+   using assertArrayAllClose following :issue:`3993`.
+   (:pull:`3994`)
+
 .. comment
     Whatsnew author names (@github name) in alphabetical order. Note that,
     core dev names are automatically included by the common_links.inc:
 
+.. _@akuhnregnier: https://github.com/akuhnregnier
 .. _@bsherratt: https://github.com/bsherratt
 .. _@larsbarring: https://github.com/larsbarring
 .. _@pdearnshaw: https://github.com/pdearnshaw
diff --git a/lib/iris/analysis/cartography.py b/lib/iris/analysis/cartography.py
index c699e7f8c4..373487af53 100644
--- a/lib/iris/analysis/cartography.py
+++ b/lib/iris/analysis/cartography.py
@@ -70,7 +70,7 @@ def wrap_lons(lons, base, period):
     # It is important to use 64bit floating precision when changing a floats
     # numbers range.
     lons = lons.astype(np.float64)
-    return ((lons - base + period * 2) % period) + base
+    return ((lons - base) % period) + base
 
 
 def unrotate_pole(rotated_lons, rotated_lats, pole_lon, pole_lat):
diff --git a/lib/iris/tests/unit/cube/test_Cube.py b/lib/iris/tests/unit/cube/test_Cube.py
index b6856bd5f2..e54ae26e1d 100644
--- a/lib/iris/tests/unit/cube/test_Cube.py
+++ b/lib/iris/tests/unit/cube/test_Cube.py
@@ -1662,11 +1662,8 @@ def test_wrap_radians(self):
         cube = create_cube(0, 360)
         cube.coord("longitude").convert_units("radians")
         result = cube.intersection(longitude=(-1, 0.5))
-        self.assertEqual(
-            result.coord("longitude").points[0], -0.99483767363676634
-        )
-        self.assertEqual(
-            result.coord("longitude").points[-1], 0.48869219055841207
+        self.assertArrayAllClose(
+            result.coord("longitude").points, np.arange(-57, 29) * np.pi / 180
         )
         self.assertEqual(result.data[0, 0, 0], 303)
         self.assertEqual(result.data[0, 0, -1], 28)