:ks is well known, scale invar iance (t) in conjunc t ion wi th Wilson 's opera to r p roduc t expans ion (2) appears to p lay an essent ia l role in t he se t t ing-up of a theore t ica l f r ame for the i n t e rp re t a t i on of expe r imen t s , such as deep inelast ic lep ton sca t te r ing , which in configurat ion space depend on the behav iour near t h e l ight-cone. I t has been sugges ted t h a t the s t ronger conformal invar iance may indeed apply in such l imit ing condi t ions and i ts impl ica t ions for equ~d-time c o m m u t a i o r s (3) and for ope ra to r p roduc t expans ions (4-e) have been discussed. In par t icu lar , in ref. (5.6) t he implicati()ns of conformal covar ianec on the opera to r p roduc t expans ion on the l ight-cone (2,7) have been fully der ived , by a m e t h o d using the Jacob i ident i t ies in ref. (4.5), and by an a l t e rna t ive mani fcs t ly covar ian t m e t h o d in ref. (s). The la t t e r m e t h o d takes advan t age of the i somorph i sm be tween the conformal a lgebra and the o r thogona l algebra O4.. , (s) aud makes use of a s ix-d imens ional pseudo-Eucl idcan co-ord ina te space. ]n th is note we shall f u r t he r develop such m e t h o d to der ive a mani fes t ly conformal covar ian t opera to r -produc t expans ion valid at all values of x 2. We n m s t s t ress t ha t , whereas conformal inva r iance (as well as scale invar iance) of the comple te t heo ry m a y in fact unde r some form hold near t he l ight-cone, wc mus t exclude the possibi l i ty t h a t the complc tc t heo ry