The Collaborative International Dictionary of English v.0.48:

Rectitude \Rec"ti*tude\ (r?k"t?*t?d), n. [L. rectitudo, fr.
   rectus right, straight: cf. F. rectitude. See Right.]
   1. Straightness. [R.] --Johnson.
      [1913 Webster]

   2. Rightness of principle or practice; exact conformity to
      truth, or to the rules prescribed for moral conduct,
      either by divine or human laws; uprightness of mind;
      uprightness; integrity; honesty; justice.
      [1913 Webster]

   3. Right judgment. [R.] --Sir G. C. Lewis.
      [1913 Webster]

   Syn: See Justice.
        [1913 Webster]

WordNet (r) 3.0 (2006):

rectitude
    n 1: righteousness as a consequence of being honorable and
         honest [syn: uprightness, rectitude]

Moby Thesaurus II by Grady Ward, 1.0:

56 Moby Thesaurus words for "rectitude":
   angelicalness, assured probity, blamelessness, character,
   cleanness, conscientiousness, correctness, decency, erectness,
   estimableness, fairness, godliness, good character, goodness,
   high ideals, high principles, high-mindedness, honesty, honor,
   honorableness, immaculacy, incorruptibility, integrity,
   irreproachability, irreproachableness, justice, justness,
   moral excellence, moral rectitude, moral strength, morale,
   morality, nobility, principle, principles, probity, propriety,
   pureness, purity, reputability, respectability, right conduct,
   righteousness, rightness, saintlikeness, saintliness,
   scrupulousness, stainlessness, unimpeachability, unimpeachableness,
   unspottedness, uprightness, upstandingness, virtue, virtuousness,
   worthiness