(1) Moral integrity. (2) Correctness of procedure.
Example:
The school superintendent wasn't popular, but no one could question her moral rectitude.
We associate straightness with honesty, so if we think someone is being misleading we might ask if they are being "straight" with us. A person whose rectitude is unquestionable is a person whose straightness, or honesty, is always apparent in his or her dealings with other people. Such a person might be called rectitudinous, although this uncommon adjective can also suggest an undesirable quality of self-righteousness.