The on-surface synthesis of single-layered covalent organic frameworks (sCOFs) has been investigated by employing a 3-fold symmetric monomer 1 carrying aldehyde groups and the ditopic diamine building block 2 on a highly oriented pyrolytic graphite surface. The self-assembly of molecule 1 is persistently observed at the stoichiometric ratio of the reactive groups. The growth of sCOF network is observed, however, only at the excess of diamine monomers. By investigating the growth process of the sCOF network, the role of excessive diamine monomers can be understood by two aspects. Increasing the molar ratio of diamine monomer provides the driving force for the structural transition from the monomer self-assembly to the formation of the sCOF network. On the other hand, the excess diamine monomers provide basic environment for the transimination reaction and promote the formation of highly ordered sCOFs. The present work provides molecular understanding of the role of transimination reaction in imine-based COF synthesis.