Retinal vein occlusion (RVO) is the second commonest retinal disease after diabetic retinopathy, and is a common cause of unilateral visual loss. There are two aims in the management of RVO: the identification of modifiable risk factors and their medical management and the recognition and management of sight-threatening complications. The management of the disease includes laser therapy and the control of systemic associated diseases. Many other treatments have been proposed but there is no evidence on their efficacy in modulating the outcome of branch or central RVO. There are currently no adequate clinical trials that have evaluated the efficacy and safety of antithrombotic agents in this setting. Antiplatelet agents are frequently used in clinical practice. Anticoagulant drugs, either heparins or coumarins, are also used in this setting as they represent the first line therapy for the treatment of venous thromboembolism. Aim of this randomized controlled study is to to compare the efficacy and safety of aspirin and of a low molecular weight heparin, parnaparin, in the treatment of RVO. Study treatment is administered for 3 months. Primary end-point of the study is the incidence of functional worsening of the eye with RVO at 6 months. Secondary efficacy outcomes are the following: proportion of cases requiring laser treatment because of the extension of the ischemic lesion and/or the presence of neovascularisation and/or macular oedema, incidence of recurrent RVO objectively documented by fluorescein angiography. Safety outcomes are defined by the incidence of major and minor bleeding events.