The Collaborative International Dictionary of English v.0.48:

Bete \Bete\ (b[=e]t), v. t.
   To better; to mend. See Beete. [Obs.] --Chaucer.
   [1913 Webster]

The Collaborative International Dictionary of English v.0.48:

Beete \Beete\, Bete \Bete\ (b[=e]t), v. t. [AS. b[=e]tan to
   mend. See Better.]
   1. To mend; to repair. [Obs.] --Chaucer.
      [1913 Webster]

   2. To renew or enkindle (a fire). [Obs.] --Chaucer.
      [1913 Webster]