above-board

Aboveboard \A*bove"board`\, adv.
   Above the board or table. Hence: in open sight; without
   trick, concealment, or deception. "Fair and aboveboard."
   --Burke.
   [1913 Webster]

   Note: This expression is said by Johnson to have been
         borrowed from gamesters, who, when they change their
         cards, put their hands under the table.
         [1913 Webster]
    

24 Moby Thesaurus words for "above-board":
      artless, candid, candidly, direct, forthright, frank, frankly,
      freely, genuine, guileless, honest, honorable, in the open,
      ingenuous, open, openly, plainly, publicly, straight,
      straightforward, straightforwardly, undeceitful, undeceiving,
      undeceptive

    

39 Moby Thesaurus words for "aboveboard":
      artless, authentic, before one, bona fide, face to face,
      fair and square, forthright, foursquare, genuine, good-faith,
      in broad daylight, in open court, in plain sight, in plain view,
      in public, in public view, in the marketplace, in the open,
      ingenuous, on the level, on the square, on the table,
      on the up-and-up, open, open and aboveboard, openly, overtly,
      plain dealing, publicly, scrupulous, single-hearted, square,
      square-dealing, square-shooting, straight, straight-shooting,
      unsophisticated, up-and-up, veritable