  We study the recursive relations for a quiver gauge theory with the gauge
group $SU(N_1)\times SU(N_2)$ with bifundamental fermions transforming as
$(N_1,\bar{N_2})$. We work out the recursive relation for the amplitudes
involving a pair of quark and antiquark and gluons of each gauge group. We
realize directly in the recursive relations the invariance under the order
preserving permutations of the gluons of the first and the second gauge group.
We check the proposed relations for MHV, 6-point and 7-point amplitudes and
find the agreements with the known results and the known relations with the
single gauge group amplitudes. The proposed recursive relation is much more
efficient in calculating the amplitudes than using the known relations with the
amplitudes of the single gauge group.
