It has been suggested that black-hole low-mass X-ray binaries (BHLMXBs) with
short orbital periods may have evolved from BH binaries with an
intermediate-mass secondary, but the donor star seems to always have higher
effective temperatures than measured in BHLMXBs (Justham, Rappaport &
Podsiadlowski 2006). Here we suggest that the secondary star is originally an
intermediate-mass (\sim 2-5 M_{\sun}) star, which loses a large fraction of
its mass due to the ejecta impact during the aspherical SN explosion that
produced the BH. The resulted secondary star could be of low-mass (\la 1
M_{\sun}). Magnetic braking would shrink the binary orbit, drive mass transfer
between the donor and the BH, producing a compact BHLMXB.Comment: 4 pages, accepted for publication in MNRAS Letter