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Definition of aboveboard : Above the board or table. Hence: in open sight; without trick, concealment, or deception.

Synonyms:

frankly, openly, artless, fair, honestly, naive, sincere, honest, unprejudiced, ingenuous, unreserved, frank, open, guileless, candid, square, simple, truthful, unbiased, unsophisticated, transparent, impartial, straight, candidly, innocent, straightforward

Usage examples:

• " He buys and sells; and his buying is not always aboveboard. - "Ashton-Kirk, Criminologist", John T. McIntyre.
• Remember, I don't know much about such things here in New York, and you must be frank and aboveboard and tell me if you have any complaints. - "Cap'n Warren's Wards", Joseph C. Lincoln.
• He looked at Metelill and said, Uncommonly pretty girl that, and knows it, but when I asked what he thought of Isabel's looks, he said, Pretty, yes; but are you sure she is quite aboveboard? - "More Bywords", Charlotte M. Yonge.