Instead you can use what's known as a spit join, or, a little less ickily, a felted join, to start the next ball of yarn.
To do this you'll need your two yarn tails, one from the working yarn and one from the new yarn, and a bit of water (yes, you can use spit, but do you really want to?).
To begin, separate each piece of yarn into two pieces. The yarn may naturally unply, or you can just pull it apart. They don't have to be completely even, you just need some more surface area to work with.
Dribble a little water on one of these separated pieces from each ball of yarn. Rub the strands between your fingers until the pieces begin to fuse together, like in felting (shown in picture above).
Do the same thing with the second side. When both parts of each end are pretty well fused together, add a little more water and rub these two joins together until it makes on cohesive strand (click picture above to see what this looks like).
Allow the yarn to dry before knitting with it and you'll have a join that's completely indistinguishable within the knitting.