We present the first observations of a square lattice formation in a monodisperse complex plasma system -a configurational transition phenomenon that has long been an experimental challenge in the field. The experiments are conducted in a tabletop L-shaped Dusty Plasma Experimental (DPEx-II) device in a DC glow discharge Argon plasma environment. By a careful control of the vertical potential confining the charged particles as well as the strength of the ion wake charge interactions with the dust particles we are able to steer the system towards a crystalline phase that exhibits a square lattice configuration. The transition occurs when the vertical confinement strength is slightly reduced below a critical value leading to a buckling of the monodisperse hexagonal 2D dust crystal to form a narrowly separated bilayer state (a quasi-2D state). Some theoretical insights into the transition process are provided through Molecular Dynamics (MD) simulations carried out for the parameters relevant to our experiment.