1. Literally, to not be at or form right angles (as or of a square). Are you blind? The foundation to this house is completely out of square!

2. By extension, to not be in agreement or alignment; to be 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.