The Minchas Chinuch (99) discussuss this in connection with the me'il
(robe) of the Cohen Gadol (High Priest). (In the new edition of the
Minchas Chinuch published by Machon Yerushalim this is on page 376. Also
see footnote #8 there.) His view is that the Cohen Gadol did not use
tzitzis, either because none of the garments had 4 four corners or,
according to the opinions that the me'il did have 4 corners, the Cohen did
not own the garments personally.
Uri Portal
e-mail: uri@iactiva.cl