diff --git a/administrator/components/com_admin/script.php b/administrator/components/com_admin/script.php
index 9b7df3f8b6684..f2eabeb3472e2 100644
--- a/administrator/components/com_admin/script.php
+++ b/administrator/components/com_admin/script.php
@@ -58,6 +58,9 @@ public function preflight($action, $installer)
 				{
 					$this->fromVersion = $manifestValues['version'];
 
+					// Ensure templates are moved to the correct mode
+					$this->fixTemplateMode();
+
 					return true;
 				}
 			}
@@ -8537,4 +8540,40 @@ protected function moveRemainingTemplateFiles()
 			}
 		}
 	}
+
+	/**
+	 * Ensure the core templates are correctly moved to the new mode.
+	 *
+	 * @return  void
+	 *
+	 * @since   __DEPLOY_VERSION__
+	 */
+	protected function fixTemplateMode(): void
+	{
+		$db = Factory::getContainer()->get('DatabaseDriver');
+
+		array_map(
+			function ($template) use ($db)
+			{
+				$clientId = $template === 'atum' ? 1 : 0;
+				$query = $db->getQuery(true)
+					->update($db->quoteName('#__template_styles'))
+					->set($db->quoteName('inheritable') . ' = 1')
+					->where($db->quoteName('template') . ' = ' . $db->quote($template))
+					->where($db->quoteName('client_id') . ' = ' . $clientId);
+
+				try
+				{
+					$db->setQuery($query)->execute();
+				}
+				catch (Exception $e)
+				{
+					echo Text::sprintf('JLIB_DATABASE_ERROR_FUNCTION_FAILED', $e->getCode(), $e->getMessage()) . '<br>';
+
+					return;
+				}
+			},
+			['atum', 'cassiopeia']
+		);
+	}
 }
diff --git a/administrator/components/com_admin/sql/updates/mysql/4.0.0-2018-03-05.sql b/administrator/components/com_admin/sql/updates/mysql/4.0.0-2018-03-05.sql
index dbae8b67ed550..c025f92818264 100644
--- a/administrator/components/com_admin/sql/updates/mysql/4.0.0-2018-03-05.sql
+++ b/administrator/components/com_admin/sql/updates/mysql/4.0.0-2018-03-05.sql
@@ -19,9 +19,11 @@ INSERT INTO `#__extensions` (`name`, `type`, `element`, `folder`, `client_id`, `
 ('atum', 'template', 'atum', '', 1, 1, 1, 0, '{}', '{}', '', '', 0, '0000-00-00 00:00:00', 0, 0),
 ('cassiopeia', 'template', 'cassiopeia', '', 0, 1, 1, 0, '{}', '{}', '', '', 0, '0000-00-00 00:00:00', 0, 0);
 
-INSERT INTO `#__template_styles` (`template`, `client_id`, `home`, `title`, `params`) VALUES
-('atum', 1, (CASE WHEN (SELECT b.`count` FROM (SELECT count(a.`id`) AS `count` FROM `#__template_styles` a WHERE a.`home` = '1' AND a.`client_id` = 1 AND a.`template` IN ('isis', 'hathor')) AS b) = 0 THEN '0' ELSE '1' END), 'atum - Default', '{}'),
-('cassiopeia', 0, (CASE WHEN (SELECT d.`count` FROM (SELECT count(c.`id`) AS `count` FROM `#__template_styles` c WHERE c.`home` = '1' AND c.`client_id` = 0 AND c.`template` IN ('protostar', 'beez3')) AS d) = 0 THEN '0' ELSE '1' END), 'cassiopeia - Default', '{}');
+-- The following statement had to be modified for 4.1 by adding the `inheritable` and `parent` columns.
+-- See https://github.com/joomla/joomla-cms/pull/36585 .
+INSERT INTO `#__template_styles` (`template`, `client_id`, `home`, `title`, `inheritable`, `parent`, `params`) VALUES
+('atum', 1, (CASE WHEN (SELECT b.`count` FROM (SELECT count(a.`id`) AS `count` FROM `#__template_styles` a WHERE a.`home` = '1' AND a.`client_id` = 1 AND a.`template` IN ('isis', 'hathor')) AS b) = 0 THEN '0' ELSE '1' END), 'atum - Default', 1, '', '{}'),
+('cassiopeia', 0, (CASE WHEN (SELECT d.`count` FROM (SELECT count(c.`id`) AS `count` FROM `#__template_styles` c WHERE c.`home` = '1' AND c.`client_id` = 0 AND c.`template` IN ('protostar', 'beez3')) AS d) = 0 THEN '0' ELSE '1' END), 'cassiopeia - Default', 1, '', '{}');
 
 --
 -- Move mod_version to the right position for the atum template
diff --git a/administrator/components/com_admin/sql/updates/postgresql/4.0.0-2018-03-05.sql b/administrator/components/com_admin/sql/updates/postgresql/4.0.0-2018-03-05.sql
index d6620523b6612..ae03fbfcb7f35 100644
--- a/administrator/components/com_admin/sql/updates/postgresql/4.0.0-2018-03-05.sql
+++ b/administrator/components/com_admin/sql/updates/postgresql/4.0.0-2018-03-05.sql
@@ -19,9 +19,11 @@ INSERT INTO "#__extensions" ("name", "type", "element", "folder", "client_id", "
 ('atum', 'template', 'atum', '', 1, 1, 1, 0, '{}', '{}', '', '', 0, '1970-01-01 00:00:00', 0, 0),
 ('cassiopeia', 'template', 'cassiopeia', '', 0, 1, 1, 0, '{}', '{}', '', '', 0, '1970-01-01 00:00:00', 0, 0);
 
-INSERT INTO "#__template_styles" ("template", "client_id", "home", "title", "params") VALUES
-('atum', 1, (CASE WHEN (SELECT b."count" FROM (SELECT count(a."id") AS "count" FROM "#__template_styles" a WHERE a."home" = '1' AND a."client_id" = 1 AND a."template" IN ('isis', 'hathor')) AS b) = 0 THEN '0' ELSE '1' END), 'atum - Default', '{}'),
-('cassiopeia', 0, (CASE WHEN (SELECT d."count" FROM (SELECT count(c."id") AS "count" FROM "#__template_styles" c WHERE c."home" = '1' AND c."client_id" = 0 AND c."template" IN ('protostar', 'beez3')) AS d) = 0 THEN '0' ELSE '1' END), 'cassiopeia - Default', '{}');
+-- The following statement had to be modified for 4.1 by adding the "inheritable" and "parent" columns.
+-- See https://github.com/joomla/joomla-cms/pull/36585 .
+INSERT INTO "#__template_styles" ("template", "client_id", "home", "title", "inheritable", "parent", "params") VALUES
+('atum', 1, (CASE WHEN (SELECT b."count" FROM (SELECT count(a."id") AS "count" FROM "#__template_styles" a WHERE a."home" = '1' AND a."client_id" = 1 AND a."template" IN ('isis', 'hathor')) AS b) = 0 THEN '0' ELSE '1' END), 'atum - Default', 1, '', '{}'),
+('cassiopeia', 0, (CASE WHEN (SELECT d."count" FROM (SELECT count(c."id") AS "count" FROM "#__template_styles" c WHERE c."home" = '1' AND c."client_id" = 0 AND c."template" IN ('protostar', 'beez3')) AS d) = 0 THEN '0' ELSE '1' END), 'cassiopeia - Default', 1, '', '{}');
 
 --
 -- Move mod_version to the right position for the atum template