Novel tri- and tetra-substituted pyrimido[4,5-d]pyridazines-2(1H,3H,7H)-ones have been synthesized via the regiospecific condensation reaction of hydrazine derivatives with 5-acetyl-4-aryloyl-6-methyl-3,4-dihydropyrimidinones in the presence of $SiO_2-Y(NO_3)_3$ as a green and recyclable catalyst under solvent-free conditions. All products were obtained in high yields and short reaction time. Employing this method is in accord with green chemistry principles.