Since you didn't specified which software you re using I'm assuming that is either ArcGIS or QGIS.
ArcGIS: you can change the Later's coordinate system by right-clicking it on the table of contents and choosing another UTM zone, this only changes the view a not the data it self. to change the data's coordinate system use the Project tool under Data Management Tools, DO NOT USE THE DEFINE PROJECTION TOOL IF YOUR DATA ALREADY HAS A PROJECT INFO! (this would mess your data beyond pretty bad) Help Docs
QGIS: right-click the data and open its properties choose a new coordinate reference system. After this just right-click the data again and re-saved it. If you only want to change the view go to Project on the top and open the project's properties, you can choose different coordinate systems there.More info
For the records: next time try to add more info on your question such as which software you are using, etc.