Discrimination of foreshock sequences from earthquake swarms is an important problem in earthquake prediction. In this paper, the magnitudes of the largest, the second largest, and the third largest shocks in an earthquake swarm or foreshock sequence are denoted by M₁, M₂, and M₃, respectively, and Japanese shallow earthquake swarms and foreshock sequences (with M₁-M₂≤0.6 and M₁≥5.0 for 1926-64 or M₁≥4.5 for 1965-77) are classified according to the values of M₁-M₂ and M₁-M₃, and the time sequence of the shocks of M₁ and M₂. If we select the earthquake swarms and foreshock sequences satisfying the following conditions, the highest proportion of foreshock sequences to earthquake swarms is achieved. The conditions are: (1) 0.4≤M₁-M₂≤0.6, (2) M₁-M₃≥0.7 (or M₃ is too small to be determined), and (3) the shock of M₂ precedes the shock of M₁. The numbers of foreshock sequences and earthquake swarms selected under these conditions are 10 and 17, respectively, while the total numbers of foreshock sequences and earthquake swarms are 13 and 232, respectively. It is confirmed that the above criterion is also effective, if it is used during the course of an earthquake sequence.