A method using a trial wave function in the form of the antisymmetrized pro
duct of strictly localized geminals (APSLG) is developed at the semiempiric
al level. The Hamiltonian is taken in the MINDO/3 form but with resonance p
arameters slightly reparametrized. The equilibrium geometries and heats of
formation of a series of organic compounds are calculated by the APSLG-MIND
O/3 method and compared with the experimental data and the results of SCF-M
INDO/3 calculations. Two different schemes of calculation of the ionization
potentials are developed and thoroughly tested. The O(N)-scalability and a
cceptable accuracy are proved for the proposed APSLG-MINDO/3 method.