The relationship between shoal size and group vigilance was investigated in the laboratory using a strongly schooling characin fish, the glowlight tetra (Hemigrammus erythrozonus). Group vigilance, as measured by the probability that at least one fish in the group detected (i.e. exhibited a startle response to) a brief, artificial alarm stimulus, increased curvilinearly at a decelerating rate with increasing shoal size. This would be predicted by the proposed early predator warning function of social groups. The observed relationship between corporate vigilance and shoal size was similar in form to one predicted by a simple signal detection model. However, observed detection probabilities for shoal sizes above 7 fish were lower than expected on the basis of this model, suggesting that an individual’s probability of detection was not always independent of shoal size nor of the probabilities of detection of other shoal members. The numbers of tetras in a shoal exhibiting a startle response to an alarm stimulus increased non-linearly with increasing shoal size and exceeded the values predicted by the above mentioned model for the larger shoals, which implies social transmission of the alarm response among shoal members. The importance of the enhanced predator detection ability of fish shoals and the social transmission of alarms within them is discussed in relation to predator avoidance behaviour and other activities of fish in shoals.