How can you treat small cut at the corner of ones eye?

Seek professional he: If you really have a cut on your eye then you should see a physician. If you have a small cut or abrasion on the skin around the eye then those will usually heal up well on their own. If you have vision changes or increasing redness see a doctor.

Choice: If it doesn't require a stitch, an antibiotic ointment is all you need and it will heal on its own.