He did so for so he did, A.V. Thy garment ( ἱμάτιον); especially the outer garment, which was worn over the χιτὼν, or tunic (see Matthew 9:20, Matthew 9:21; Matthew 14:36; Matthew 23:1-39. 5, etc.).
The girding, therefore, applied to the inner garments, and περιβαλοῦ to the cloak which went over them.