Formaldehyde emission from wood-based products has been a threat to human health and the environment due to the use of formaldehyde-based adhesives. Glyoxal (G) was once regarded as a promising substitute for formaldehyde due to its formaldehyde-like reactivity and low toxicity. However, many studies have indicated that the urea-glyoxal (UG) and melamine-glyoxal (MG) reactions did not lead to the desired adhesion property due to cyclization reactions. To prevent cyclization, in this study, a long-chain melamine-1,6-hexanediamine (MH) polymer was used with glyoxal to fabricate wood adhesive via a facile and clean strategy. In contrast to previously reported glyoxal-related wood adhesives, the MHG adhesive exhibited a lower cure temperature, much higher bonding strength, and far superior water resistance. Particularly, when a low hot-press temperature of 80 °C was applied, a dry bonding strength above 2.42 MPa (100% wood failure) and a wet bonding strength (boiling in water for 3 h) of 1.62 MPa were achieved for plywood. With a higher cure temperature of 120 °C applied, a bonding strength above 1.50 MPa was retained with 100% wood failure even after boiling for 72 h. Structural characterizations suggested that the outstanding performances of the MHG adhesive can be attributed to easy formation of highly stable conjugated imine bonds (−N�C−C�N−).