MODEL RELEASED. Red eye (subconjunctival haemorrhage) caused by bleeding beneath the conjunctiva, the transparent membrane that covers the eye. The bleeding may be due to a blow, but often it is caused by the rupture of a blood vessel after coughing or straining. It can also occur if the patient is taking anticoagulant drugs such as warfarin. The condition is painless and generally clears up without medical intervention.