These are (close to) the right amplitudes to actually produce a square wave from an infinite number of odd harmonics. Somewhat short of infinity, we only have 4 harmonics here, but it proves the point that it could be done with infinite harmonics. (If you get more overshoot with more harmonics, they're not scaled correctly.)
To make +-1v square wave:
1khz 1.23v
3khz 388mv
5khz 209mv
7khz 125mv
9khz 76mv
No phase shift
Derivation of the amplitudes:
http://everycircuit.com/circuit/6122013801578496
