Flow (of a Newtonian and incompressible fluid) separation around a square cylinder for Reynolds numbers (Re) in the range of 10-400 is investigated through direct numerical simulations. In contrast to the general belief that for a square cylinder, the flow would always separate at the leading and/or trailing edges of the cylinder, this study shows that the flow (both time-averaged and instantaneous) may not separate at the sharp corners for a certain range of moderate Re values. Instead, separation emerges at approximately a quarter of the cylinder length downstream of the leading edge at critical Re values of 100.36 and 96 for the time-averaged and instantaneous flows, respectively. With the increase in Re, the time-averaged separation location gradually moves toward the leading edge, while its instantaneous variation range reduces. The evolution of the separation pattern with Re is categorized with a fine Re resolution of 1. A critical point is identified at Re = 156 (for the time-averaged flow), where a saddle point emerges away from the upper/lower surface of the cylinder to give rise to wake flow entrainment to the upper/lower side of the cylinder. The rate of the entrained flow is governed by the location of the saddle point. The flow three-dimensionality occurring at Re > 165.7 affects the location of the saddle point but has almost no influence on the location of the separation point. The corresponding physical mechanism is explained.