I'm having a little trouble picturing exactly what's happening. But if you think the problem is at your first stitch and where the yarn is, you may be wrapping the yarn around the shaft of the right needle, making an extra stitch there. If there's loop at the end of the row, that might be it.
Before you put your needle in for the first stitch, make sure the yarn is behind both needles for knit or in front of both needles for purl.
If this isn't the problem, is there any way you can post a picture?