>Try

SELECT * FROM mytable m1
>  WHERE UniqueId IN
>    ( SELECT MIN(UniqueId) FROM mytable m2 WHERE m2.GroupField = m2.GroupField )
>

Or

SELECT MIN(UniqueId) AS UniqueId, GroupField1, GroupField2 ;
>  FROM mytable
>  GROUP BY GroupField1, GroupField2 ;
>  INTO CURSOR crsMin
>
>SELECT *  ;
>  FROM mytable
>  WHERE UniqueId + GroupField1 + GroupField2 IN ( ;
>    SELECT UniqueId + GroupField1 + GroupField2 FROM crsMin ) ;
>  INTO CURSOR crsResult
>

Yes, as I need additional fields and they should match the record that has been selected, I need to do that in two steps. Either such as you did or doing a small scan after to adjust some fields.