In a decisive, thoroughgoing, or open and legitimate manner; with full and honest effort or outright success; fair and square. Also as a general intensifier: very, exceptionally, completely. Cf. fair dinkum adv.
“square dinkum, adv., adj., and n. (and int.).” OED Online, Oxford University Press, January 2018, www.oed.com/view/Entry/412323. Accessed 22 March 2018.
I noticed that there aren’t very many adverbs in general. Not sure if that’s true for the entire English language.