Square atomic configurations of two-dimensional gold and platinum are designed on the basis of density functional theory calculations. Calculations reveal that Au9 and Pt9 clusters form energetically stable perfect square structures. Combining and alternating two Au9 and two Pt9 allows for the formation of infinite square two-dimensional sheets of Au9, Pt9, and Au18Pt18. The electronic density of state reveals that two-dimensional Au9, Pt9, and Au18Pt18 retain metallic characteristics whereas two-dimensional Pt9 and Au18Pt18 also possess magnetic properties. In addition, the multilayered two-dimensional Au9 and Au18Pt18 of up to five layers and four layers, respectively, are designed. Two dimensional Au9, Pt9, and Au18Pt18 could have potential applications toward filtering gases or impurities in liquids as well as electronics.