We have reexamined accretion in a protobinary system with two dimensional numerical simulations. We consider protostars which rotate around the center of the mass with circular orbits. The accreting gas is assumed to flow in the orbital plane. It is injected from a circle whose radius is 5 times larger than the orbital separation of the binary. The injected gas has constant surface density, in fall velocity, and specific angular momentum. The accretion depends on the specific angular momentum of the injected gas, j
inf. When j
inf is small, the binary accretes the gas mainly through two channels: one through the Lagrangian point L2 and the other through L3. When j
inf is large, the binary accretes the gas only through the L2 point. The primary accretes more than the secondary in both cases, although the L2 point is closer to the secondary. After flowing through the L2 point, the gas flows half around the secondary and through the L1 point to the primary. Only a small amount of gas flows back to the secondary and the rest forms a circumstellar ring around the primary. The accretion decreases the mass ratio, q = M
1, where M
1 and M
2 denote the masses of the primary and secondary, respectively. The accretion rate increases with time. When j
inf is large, it is negligibly small in the first few rotation periods.