I have a 100% cotton table cloth and washed it on full cycle with about 1/2 cup of bleach. It came out yellow. I've tried vinegar wash, soda wash, with salt, hanging it outside in the sun and to no avail it's still yellow looking. Needless to say all the other linens came out fine.
I read somewhere that if white garment was pre-treated with a whitening agent, that the manufacturer says you shouldn't use bleach on it for it would turn it yellow. It sounds as if this has happened in your case.
I sounds as though the cloth may contain something other than 100% cotton (regardless if the tag says otherwise), like nylon or other non-organic fiber. I would probably put it back out in the sunshine, turning it every day for a week or more.
You might also try using a "bluing" agent, such as Mrs. Stewart's Bluing.
I've whitened dingy whites by using Oxyclean and boiling water. I make a strong solution and soak my things in this for hours (sometimes overnight) and they come out white again. It really worked well on some things my grandmother made 77 years ago and didn't damage them.
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