diff --git a/htdocs/install/mysql/migration/3.6.0-3.7.0.sql b/htdocs/install/mysql/migration/3.6.0-3.7.0.sql
index 5e633eb2660..b6640f1a4c9 100644
--- a/htdocs/install/mysql/migration/3.6.0-3.7.0.sql
+++ b/htdocs/install/mysql/migration/3.6.0-3.7.0.sql
@@ -1088,7 +1088,8 @@ ALTER TABLE llx_usergroup_extrafields ADD INDEX idx_usergroup_extrafields (fk_ob
 
 ALTER TABLE llx_contrat ADD COLUMN model_pdf varchar(255) DEFAULT NULL AFTER note_public;
 
-ALTER TABLE llx_c_email_templates ADD UNIQUE INDEX uk_c_email_templates(label, lang);
+ALTER TABLE llx_c_email_templates DROP INDEX uk_c_email_templates;
+ALTER TABLE llx_c_email_templates ADD UNIQUE INDEX uk_c_email_templates(entity, label, lang);
 ALTER TABLE llx_c_email_templates ADD INDEX idx_type(type_template);
 
 -- Remove OSC module
diff --git a/htdocs/install/mysql/tables/llx_c_email_templates.key.sql b/htdocs/install/mysql/tables/llx_c_email_templates.key.sql
index f4a632e9afc..665b8d610f0 100644
--- a/htdocs/install/mysql/tables/llx_c_email_templates.key.sql
+++ b/htdocs/install/mysql/tables/llx_c_email_templates.key.sql
@@ -17,6 +17,6 @@
 -- Table with templates of emails
 -- ===================================================================
 
-ALTER TABLE llx_c_email_templates ADD UNIQUE INDEX uk_c_email_templates(label, lang);
+ALTER TABLE llx_c_email_templates ADD UNIQUE INDEX uk_c_email_templates(entity, label, lang);
 ALTER TABLE llx_c_email_templates ADD INDEX idx_type(type_template);