Dissymmetric reactions, which enable differentiated functionalization of equivalent sites within one molecule, have many potential applications in synthetic chemistry and materials science, but they are very challenging to achieve. Here, the dissymmetric reaction of 1,4-dibromo-2,5-diethynylbenzene (2Br-DEB) on Ag(111) is realized by using a stepwise activation strategy, leading to an ordered two-dimensional organometallic network containing both alkynyl-silver-alkynyl and alkynyl-silver-phenyl nodes. Scanning tunneling microscopy and density functional theory calculations are employed to explore the stepwise conversion of 2Br-DEB, which starts from the H-passivation of one Br-substituted site at 300 K in accompaniment with an intermolecular reaction to form one-dimensional organometallic chains containing alkynyl-silver-alkynyl nodes. Afterwards, the other equivalent Br-substituted site undergoes metalation reaction at 320-450 K, resulting in transformation of the chains into the binodal networks. These findings exemplify the achievement of the dissymmetric reaction and its practical application for controlled fabrications of complicated yet ordered nanostructures on a surface.