This is a pretty good technique, but there are problems with it.  Using derived tables in a query can be very powerful, but they can also cause excessive use of tempdb (similar to using # tables).  Often, there are other ways of doing the same thing for cheaper.

So, if you don't have to use them, don't.  The query below is functionally equivalent to the delete statement in the article, but it costs almost half.

delete p1
From Payment p1
JOIN Payment p2
   on  p1.CustomerNumber = p2.CustomerNumber and
    p1.PostedDateTime = p2.PostedDateTime and
    p1.PaymentAmt   = p2.PaymentAmt
where p1.PaymentID < p2.PaymentID

Here's the full script:

if object_ID('tempdb..#Payment') is not null drop table #Payment
CREATE TABLE #Payment(
 PaymentID int identity Not nUll Primary Key,
 CustomerNumber int  NOT NULL,
 PostedDatetime datetime NOT NULL,
 PaymentAmt money  NOT NULL,
 PaymentMemo varchar(200) NOT NULL,
 CCRefNum char(10) NOT NULL
)

Insert #Payment Values (1, '01/01/2004', 1, '', '')
Insert #Payment Values (1, '01/01/2004', 1, '', '')
Insert #Payment Values (2, '01/02/2004', 2, '', '')
Insert #Payment Values (2, '01/02/2004', 2, '', '')
Insert #Payment Values (2, '01/02/2004', 2, '', '')
Insert #Payment Values (3, '01/03/2004', 3, '', '')
Insert #Payment Values (3, '01/03/2004', 3, '', '')
Insert #Payment Values (3, '01/03/2004', 3, '', '')
Insert #Payment Values (3, '01/03/2004', 3, '', '')

delete p1
From #Payment p1
JOIN #Payment p2
   on  p1.CustomerNumber = p2.CustomerNumber and
    p1.PostedDateTime = p2.PostedDateTime and
    p1.PaymentAmt   = p2.PaymentAmt
where p1.PaymentID < p2.PaymentID

DELETE FROM
 p1
FROM
 #Payment p1
INNER JOIN
 (
  SELECT
   MAX(PaymentID) AS PaymentID,
   CustomerNumber,
   PostedDatetime,
   PaymentAmt
  FROM
   #Payment
  GROUP BY
   CustomerNumber,
   PostedDatetime,
   PaymentAmt
  HAVING
   COUNT(*) > 1
  p2
 ON(
  p1.CustomerNumber = p2.CustomerNumber
  AND
  p1.PostedDatetime = p2.PostedDatetime
  AND
  p1.PaymentAmt = p2.PaymentAmt
  AND
  p1.PaymentID <> p2.PaymentID