Green’s Dictionary of Slang

squarehead n.1

[square adj. (2) + -head sfx (1)]

1. [mid-19C+] an honest person, a respectable person.

2. [1910s+] a stupid person.

3. [1920s+] (Aus.) a timid or conscience-ridden thief.

4. [1930s+] (Aus.) one who has no previous criminal convictions.