diff --git a/changelogs/unreleased/296756-cablett-remove-index.yml b/changelogs/unreleased/296756-cablett-remove-index.yml
new file mode 100644
index 0000000000000000000000000000000000000000..a0d19eb24bdf37eb71626ec4409c10e1e5c43819
--- /dev/null
+++ b/changelogs/unreleased/296756-cablett-remove-index.yml
@@ -0,0 +1,5 @@
+---
+title: Remove inconsistent index in backup_labels table
+merge_request: 53189
+author:
+type: other
diff --git a/db/migrate/20210203002331_drop_backup_label_index.rb b/db/migrate/20210203002331_drop_backup_label_index.rb
new file mode 100644
index 0000000000000000000000000000000000000000..430d2d0fb79609e16aab92800b5e7bf345d63662
--- /dev/null
+++ b/db/migrate/20210203002331_drop_backup_label_index.rb
@@ -0,0 +1,19 @@
+# frozen_string_literal: true
+
+class DropBackupLabelIndex < ActiveRecord::Migration[6.0]
+  include Gitlab::Database::MigrationHelpers
+
+  DOWNTIME = false
+
+  disable_ddl_transaction!
+
+  INDEX_NAME = 'backup_labels_project_id_title_idx'
+
+  def up
+    remove_concurrent_index_by_name(:backup_labels, name: INDEX_NAME)
+  end
+
+  def down
+    add_concurrent_index :backup_labels, [:project_id, :title], name: INDEX_NAME, unique: true, where: 'group_id = NULL::integer'
+  end
+end
diff --git a/db/schema_migrations/20210203002331 b/db/schema_migrations/20210203002331
new file mode 100644
index 0000000000000000000000000000000000000000..f1ed6bf23f685fa6dd765159d20411570121d008
--- /dev/null
+++ b/db/schema_migrations/20210203002331
@@ -0,0 +1 @@
+b8a19b2ebf648a1b79a488a7a2847f6a392e594464c1ba0ae96f274f583559e3
\ No newline at end of file
diff --git a/db/structure.sql b/db/structure.sql
index 017ef14931f4246a8e1521bdf6f9ea11917ab30c..16abc7379755148848f0936b5803a7db1cfc6dd1 100644
--- a/db/structure.sql
+++ b/db/structure.sql
@@ -21025,8 +21025,6 @@ CREATE INDEX backup_labels_group_id_title_idx ON backup_labels USING btree (grou
 
 CREATE INDEX backup_labels_project_id_idx ON backup_labels USING btree (project_id);
 
-CREATE UNIQUE INDEX backup_labels_project_id_title_idx ON backup_labels USING btree (project_id, title) WHERE (group_id = NULL::integer);
-
 CREATE INDEX backup_labels_template_idx ON backup_labels USING btree (template) WHERE template;
 
 CREATE INDEX backup_labels_title_idx ON backup_labels USING btree (title);