SQL UPDATE column with self referenced id from another column

I want to update the ParentId of each row that is not null

With the Id from the row that has a TemplateId Matching ParentId

Id	ParentId	TemplateID
1001	NULL	86
1002	86	41
1003	43	44
1004	NULL	43
1005	44	73

Desired results:

Id	ParentId	TemplateID
1001	NULL	86
1002	1001	41
1003	1004	44
1004	NULL	43
1005	1003	73

The way I am doing it seems extremely convoluted. Is there a simpler way?

  UPDATE
    [dbo].[tbl]
  SET
    [ParentID] = [z].[ItemID]
  FROM
    [dbo].[tbl]
  JOIN (
    SELECT
      [x].[ParentID]
    FROM
      [dbo].[tbl]
    JOIN (
      SELECT DISTINCT
        [ParentID]
      FROM
        [dbo].[tbl]
      WHERE
        [ParentID] > 0
    ) [x]
    ON
      [dbo].[tbl].[TemplateID] = [x].[ParentID]
  ) [z]
  ON
    [dbo].[tbl].[ParentID] = [z].[ParentID]

Answer

This should gives you what you want. Self Join with ParentID = TemplateID

---

UPDATE t1
SET    ParentID = t2.ItemID
FROM   tbl t1
       INNER JOIN tbl t2 ON t1.ParentID = t2.TemplateID

dbfiddle demo