2001 Chevy S-10 voltage

Electrical problem
2001 Chevy S-10 4 cyl Two Wheel Drive Automatic

I put in a new battery and the alternator checks out good (it is only a month old). When the engine starts, within 5 minutes the voltage is so low that the engine dies. The voltage starts out at 13 or 14 but goes down quickly. I have checked the wiring that I can get to and nothing appears to be wrong. Help!