A Direct Numerical Simulation (DNS) study of an axisymmetric turbulent wake generated by a square plate placed normal to the incoming flow is presented. It is shown that the new axisymmetric turbulent wake scalings obtained recently for a fractal-like wake generator (Dairay et al., 2015), specifically a plate with irregular multiscale periphery placed normal to the incoming flow, are also present in an axisymmetric turbulent wake generated by a regular square plate. These new scalings are therefore not caused by the multiscale nature of the wake generator but have more general validity.