1. Literally, not at or forming right angles (as or of a square). Are you blind? The foundation to this house is completely out of square! The house has a couple of door frames out of square, but otherwise, it's a fine example of carpentry.

2. By extension, not in agreement or alignment; faulty or not in proper order. Environmentalists are claiming that the study on climate change, backed largely by the oil industry, is completely out of square with the truth. Everything about this project has been out of square from the beginning—I think it's time we just started the whole thing over.