Subconjunctival hemorrhage is a bright red patch appearing in the white of the eye. This condition is also called red eye. A subconjunctival hemorrhage occurs when a small blood vessel breaks open and bleeds near the surface of the white of the eye (bulbar conjunctiva). It may happen without injury, and is often first noticed when you wake up and look in a mirror. A bright red patch appears on the white of the eye which does not cause pain .If you have other areas of bleeding or bruising, more specific tests may be needed. Your blood pressure regularly should be checked as treatment.