The experimental results of the susceptibility, specific heat, magnetization, and electron spin resonance of Cu(H2O)(2)(C2H8N2)SO4 are reported. Despite the triangular arrangement of chemical bonds, the system is identified as an S=1/2 Heisenberg antiferromagnet where the dominant exchange coupling J/k(B)approximate to-1.4 K is mediated by a square network of hydrogen bonds. The long-range ordering observed at T-N=0.91 K is proposed to be Neel type. The possibility of tuning the strength of the exchange couplings in various directions is discussed.