Rectitude
Etymology
From Latin rectitudo, "straightness," built on rectus, "straight, right," the past participle of regere, "to guide, keep straight, rule." The metaphor is spatial before it is moral: a life without bends or crookedness. English inherited both senses, but the moral one — uprightness of character — is now the living meaning.
noun · /REK-tih-tood/
Strict correctness and moral uprightness in conduct, judgment, and principle.
What it names
The quality of a person who keeps to a straight moral line — used when you want to stress adherence to principle rather than warmth or charm.
Example
His rectitude was admirable and slightly exhausting; he would not fudge an expense report to save his own job.
Related idea
Probity stresses tested honesty, especially with money and trust; rectitude is broader, naming an overall straightness of principle and conduct.