The dinuclear complex 1 with cooperative hydrogen bonds can be prepared by the metal-directed reaction of Eq. (2). This work shows that the coordinated hydroxyl group trans to the secondary amino group is deprotonated more readily than that trans to the tertiary amino group and acts as the hydrogen-bond accepter. The lattice water molecules in 1 act as bridges between the two mononuclear units through hydrogen bonds. The complex is quite stable as the dimeric form even in various polar solvents. The complex exhibits a weak antiferromagnetic interaction between the metal ions in spite of relatively long Cu$cdots$Cu distance. This strongly supports the suggestion that the antiferromagnetic behavior is closely related to the cooperative hydrogen bonds.