A.T. Robertson Commentary 1 Corinthians 11:4

"Every man praying or prophesying, having his head covered, dishonoreth his head." — 1 Corinthians 11:4 (ASV)

Having his head covered (κατα κεφαλης εχων). Literally, having a veil (καλυμμα understood) down from the head (κεφαλης ablative after κατα as with κατα in Mr 5:13; Acts 27:14). It is not certain whether the Jews at this time used the tallith, "a four-corned shawl having fringes consisting of eight threads, each knotted five times" (Vincent) as they did later. Virgil (Aeneid iii., 545) says: "And our heads are shrouded before the altar with a Phrygian vestment." The Greeks (both men and women) remained bareheaded in public prayer and this usage Paul commends for the men.