This is one of the blocks my friend found that her grandmother had made. She has 20 blocks like this; different colors, but same bleached muslin background. Does anyone here know the name of this block?

I have no idea, but it looks like a simple block. It looks like one I could even do. Sorry can't be of help.

Rita

It looks like a variation of a Shoo-fly block. A 4 patch for the center with the 'shoo-fly' on the outside. Great block!

A friend from highschool had seen my quilts on Facebook. She found 20 of these squares, a Trip around the World, and a Lone Star. She wants to try finishing at least one of them herself, but she is not the kind to sit down for very long! I thought if we could get these squares into a quilt, it would be easier than trying to finish the other ones, especially since it looks like we have to take a panel out of the Lone Star to get it to lie flat. She does sew some, but mainly making drapes. Seems to me quilting would be a whole lot easier! She's going to go through more of her grandmother's things to see if she can find any more treasures. I was as excited as she was!

Looks like a variation on that block of many names: Churndash, Shoo-fly, Monkeewrench............ there are probably more!
Just reading about the problem with the Lone Star makes me wonder if Sharon Schambers blocking technique combined with a lot of quilting might save you some aggravation.....

I'd say a 9-patch variation - but it's only a guess