Green’s Dictionary of Slang

1. an honest person, a conventionable, respectable person.

1864		J. Armour Diggings, the Bush, and Melbourne 16: I learnt that nearly all the company had been ‘Government men,’ as convicts style themselves. [...] [and] being a ‘square head,’ that is one outside of their community, I would readily be suspected if were tales told.
1886		Bulletin (Sydney) 31 July 7/4: [O]ing to ill-luck, brought on by associating with a ‘square-head,’ the ‘demon put pincher on him.’.
1895		Truth (Sydney) 12 May 5/7: I shouldn’t have anticipated much less luck for a ‘Square-head’ unfortunate to get into the clutches of such a cute and foxy trickster.
1900		Sydney Sportsman (Surry Hills, NSW) 10 Oct. 1/1: Square heads won’t squeal at my notes, and as for the cronk crew, I like to hear them squeak.
1939		K. Tennant Foveaux 312: ‘What’s y’r old man do for a crust?’ Curly asked. ‘Works,’ Neicie answered shortly. ‘Drives a taxi.’ Curly raised his eyebrows. ‘A squarehead.’.
1954		Sun. Mail (Adelaide) 25 Sept. 45/7: I always sought rhe company of ‘square heads’, men who have had no trouble with the law.
1967		‘Whisper All Aussie Dict.’ in Kings Cross Whisper (Sydney) xxxix 4/5: square head: A conformist.
1983		R. Aven-Bray Ridgey-Didge Oz Jack Lang 45: Squareheads Non-criminals.
1986		R.G. Barrett Real Thing 99: Norton, being a bit of a square-head, Queensland country boy [etc.].
1990		see sense 2.
1998		P. Doyle (con. late 1950s) Amaze Your Friends (2019) 122: Some squareheads from the Billy Graham Crusade.
2005		M.B. ‘Chopper’ Read Chopper 4 15: I’ve never really mixed with squareheads and normal people.

2. a stupid person.

1913–14		Van Loan ‘No Business’ in Taking the Count 149: He handed that big squarehead from the revenue cutter an awful trimming.
1916		P. Kyne Cappy Ricks 20: I’ll dig up a bosun among the squareheads.
1937		P. Ernst ‘The Chair Cheater’ in Phantom Detective Jan. 🌐 You squarehead—we’ve only got one coffin aboard, ain’t we?
1955		B. Hill Boss of Britain’s Underworld 89: I was not like that bunch of swedes and squareheads they had in there from provincial towns.
1958		F.J. Hardy Four-Legged Lottery 86: Look who’s here, the square head from the library.
1989		H. Rawson Dict. of Invective (1991) 372: The older squarehead, a stupid person.
1990		Tupper & Wortley Aus. Prison Sl. Gloss. 🌐 Squarehead. A naive or uncorrupted person. Thus someone doing prison for the first time who doesn’t understand the prison values and lives according to the values of society outside: or a straight (non-gaol) person.

3. (Aus.) a timid or conscience-ridden thief.

1941

Baker Popular Dict. Aus. Sl.

4. (Aus.) one who has no previous criminal convictions.

1950		S.J. Baker in Sun. Herald (Sydney) 8 June 9/2: There’s [...] the ‘cleanskin,’ ‘squarehead’ or ‘squarey,’ the new crook who has had no previous convictions.
1967		‘Whisper All Aussie Dict.’ in Kings Cross Whisper (Sydney) xxxix 4/5: square head: [...] An unconvicted person.
1984		B. Ellem Doing Time 24: When I first come in I was conned a lot, I suppose I was a real sucker, a square head, and the other crims took me down for what they could.