"in open sight, without trickery or disguise," 1610s, from above and board (n.1). "A figurative expression borrowed from gamesters, who, when they put their hands under the table, are changing their cards." [Johnson]
was known for dealing aboveboard in everything
their business was open and aboveboard
abortive
abound
abounding
about
above
aboveboard
abovementioned
abracadabra
abrade
Abraham
abrasion