Slip 1 stitch knitwise from left needle to right needle, then (slip 1 stitch knitwise from left needle to right needle, pass second stitch on right needle over first stitch) three/four times. You have just bound off three/four stitches. No, you don’t knit these stitches first. Yes, they create a slightly stiff edge. This is exactly what is needed.
Return last stitch on right needle to left needle. This opens up the whole you just made.
Turn work so that wrong side is facing, and bring yarn between the needles to the front. Note here: if I were making a buttonhole on a garter stitch band, I would leave the yarn in back.
*Purl into first stitch on left needle, the slip new stitch onto left needle; repeat from * until four/five stitches have been made, and are sitting on the left needle. If this doesn’t seem quite tight enough, and it does need to be firm, purl each new stitch through the back loop. For this sweater, I bound off three stitches, and I cast on four for a three-stitch buttonhole. Also, if I were making a garter stitch button band, I would knit stitches on, instead of purling them, and I would definitely knit into the back loop for the additional firmness.
Turn so that right side is facing you again, and yarn is in back. Slip first stitch from left needle to right needle, pass second stitch on right needle over slipped stitch. This closes up the unsightly gap that is left by so many other buttonhole techniques.
Voila! The buttonhole is done. It sometimes still seems a little iffy, insubstantial, until I have some fabric on the far side, but once the ribbing is all done, and everything has been bound off, this buttonhole shines.