Current computational models of visual salience accurately predict the distribution of fixations on isolated visual stimuli. It is not known, however, whether the global salience of a stimulus, that is, its effectiveness in the competition for attention with other stimuli, is a function of the local salience or an independent measure. Further, do task and familiarity with the competing images influence eye movements? Here, we investigated the direction of the first saccade to characterize and analyze the global visual salience of competing stimuli. Participants freely observed pairs of images while eye movements were recorded. The pairs balanced the combinations of new and already seen images, as well as task and task-free trials. Then, we trained a logistic regression model that accurately predicted the location-left or right image-of the first fixation for each stimulus pair, accounting too for the influence of task, familiarity, and lateral bias. The coefficients of the model provided a reliable measure of global salience, which we contrasted with two distinct local salience models, GBVS and Deep Gaze. The lack of correlation of the behavioral data with the former and the small correlation with the latter indicate that global salience cannot be explained by the feature-driven local salience of images. Further, the influence of task and familiarity was rather small, and we reproduced the previously reported left-sided bias. Summarized, we showed that natural stimuli have an intrinsic global salience related to the human initial gaze direction, independent of the local salience and little influenced by task and familiarity.