surely, singapore al flies to bejing?....i'm not experienced in that area, but, my first action would be see what comes up when i try to price the whole iten....often, it will show a number of a/l's that fly the legs....

what does expensive mean?....good luck...

edit to add....it looks like air china & singapore al do non stops....however, you might want to come back from bejing, rather than going back to sin....i would look into putting the whole trip on 1 ticket....might be cheaper...