Magnetization reversal was studied in square arrays of square Co/CoO dots with lateral size varying between 200 and 900 nm. While reference nonpatterned Co/CoO films show the typical shift and increased width of the hysteresis loop due to exchange bias, the patterned samples reveal a pronounced size dependence. In particular, an anomaly appears in the upper branch of the magnetization cycle and becomes stronger as the dot size decreases. This anomaly, which is absent at room temperature in the patterned samples, can be understood in terms of a competition between magnetostatic interdot interaction and exchange anisotropy during the magnetic switching process.