The Collaborative International Dictionary of English v.0.48:

Improper \Im*prop"er\, a. [F. impropre, L. improprius; pref. im-
   not + proprius proper. See Proper.]
   1. Not proper; not suitable; not fitted to the circumstances,
      design, or end; unfit; not becoming; incongruous;
      inappropriate; indecent; as, an improper medicine;
      improper thought, behavior, language, dress.
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            Follow'd his enemy king, and did him service,
            Improper for a slave.                 --Shak.
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            And to their proper operation still,
            Ascribe all Good; to their improper, Ill. --Pope.
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   2. Not peculiar or appropriate to individuals; general;
      common. [Obs.]
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            Not to be adorned with any art but such improper
            ones as nature is said to bestow, as singing and
            poetry.                               --J. Fletcher.
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   3. Not according to facts; inaccurate; erroneous.
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   Improper diphthong. See under Diphthong.

   Improper feud, an original feud, not earned by military
      service. --Mozley & W.

   Improper fraction. See under Fraction.
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The Collaborative International Dictionary of English v.0.48:

Diphthong \Diph"thong\ (?; 115, 277), n. [L. diphthongus, Gr. ?;
   di- = di`s- twice + ? voice, sound, fr. ? to utter a sound:
   cf. F. diphthongue.] (Ortho["e]py)
      (a) A coalition or union of two vowel sounds pronounced in
          one syllable; as, ou in out, oi in noise; -- called a
          proper diphthong.
      (b) A vowel digraph; a union of two vowels in the same
          syllable, only one of them being sounded; as, ai in
          rain, eo in people; -- called an improper diphthong.
          [1913 Webster]