Kitchener stitch on 1×1 rib will end up with a jog in the stitches unless you prepare your provisional cast-on exactly right. This videos shows each step to setting up and doing Kitchener stitch correctly on 1×1 rib without any headaches.
Video: How to Do Kitchener Stitch on 1×1 Rib
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These instructions show how to seamlessly join 1x1 rib top-to-bottom, that is, when you join provisional cast-on stitches to the edge to be bound off. These instructions will not work for top-to-top seaming, for instance, where you would fold the working edge of your work and seam it together.
For a technical explanation of why this works (and how to graft 1x1 ribbing top-to-top) I recommend Joni Coniglio's Interweave article Grafting Knitting, Myth 2: Grafted Ribbing Will Always Have a Half-Stitch Jog.
For a step-by-step photo tutorial of Kitchener stitch, a downloadable cheat sheet, and lots of Kitchener stitch tips and tricks, see our Complete Video Guide to Seaming Your Knitting With Kitchener Stitch.
Cast on your ribbing using a provisional cast-on.
When you are ready to bind off, cut the loops of your provisional cast-on. Feed knitting needle through the loops the provisional cast-on has saved, making sure to get the half-loop on either side.
You will need to capture the tail of the working piece that will be loose and weave it into the side of your work, anchoring the last half-loop.
You should have one more loop on the provisional cast-on needle than you do on your working needle. In the example in the video, there are 6 loops on the provisional needle and 5 on the working needle.
Orient your knitting so that the needle tips face to the right. The provisional cast-on needle should be in the back.
Cut your yarn to 3x the width of the stitches to be bound off, plus 6 inches for weaving in. Thread onto a tapestry needle.
There are no setup stitches for Kitchener stitch on 1x1 rib. Work the sequence according to what kind of stitch you are binding off on the front needle.
For a knit stitch:
Front needle: Feed tapestry needle through purlwise. Do not remove stitch.
Back needle: Feed tapestry needle through purlwise. Remove stitch.
Back needle: Feed tapestry needle through knitwise. Do not remove stitch.
Front needle: Feed tapestry needle through knitwise. Remove stitch.
For a purl stitch:
Front needle: Feed tapestry needle through knitwise. Do not remove stitch.
Back needle: Feed tapestry needle through knitwise. Remove stitch.
Back needle: Feed tapestry needle through purlwise. Do not remove stitch.
Front needle: Feed tapestry needle through purlwise. Remove stitch.