Correlated firing among neurons is widespread in the visual system. Neighbouring neurons, in areas from retina to cortex, tend to fire together more often than would be expected by chance. The importance of this correlated firing for encoding visual information is unclear and controversial. Here we examine its importance in the retina. We present the retina with natural stimuli and record the responses of its output cells, the ganglion cells. We then use information theoretic techniques to measure the amount of information about the stimuli that can be obtained from the cells under two conditions: when their correlated firing is taken into account, and when their correlated firing is ignored. We find that more than 90% of the information about the stimuli can be obtained from the cells when their correlated firing is ignored. This indicates that ganglion cells act largely independently to encode information, which greatly simplifies the problem of decoding their activity.