The concept of resonance-assisted hydrogen bond (RAHB) has been widely accepted, and its impact on structures and energetics can be best studied computationally using the block-localized wave function (BLW) method, which is a variant of ab initio valence bond (VB) theory and able to derive strictly electron-localized structures self-consistently. In this work, we use the BLW method to examine a few molecules that result from the merging of two malonaldehyde molecules. As each of these molecules contains two hydrogen bonds, these intramolecular hydrogen bonds may be cooperative or anticooperative, depended on their relative orientations, and compared with the hydrogen bond in malonaldehyde. Apart from quantitatively confirming the concept of RAHB, the comparison of the computations with and without pi resonance shows that both sigma-framework and pi-resonance contribute to the nonadditivity in these RAHB systems with multiple hydrogen bonds.