A removable orthodontic appliance of discrete plastic sleeves, each being receivable over a corresponding tooth of a patient. Lingual clips are fastened to the corresponding tooth and which are engageable with corresponding structure of the sleeves for removably retaining each of said plastic sleeves to the corresponding tooth of the patient. Buccal brackets are fixably carried on a side of each of the sleeves positionally corresponding to a buccal surface of the corresponding tooth to which each of the sleeves is receivable. An arch wire is ligated to each of the buccal brackets to extend therebetween. The system can be conveniently removed for cleaning and adjustment.