Immediately following Batman #1, DC Editor Whitney Ellsworth spoke to Bob Kane and Bill Finger. From now on, Batman would be against killing, a rule Superman's creators had already applied to their own creation. Ellsworth added, "Never let us have Batman carry a gun again."
Ellsworth wanted Batman to rise above his pulp vigilante roots and become a genuine superhero, someone who seemed at home in a world also inhabited by Superman and the rising number of similarly colorful champions. By this time, Finger and Kane had introduced young Dick Grayson as Batman's new apprentice, a cheerful, acrobatic detective who provided some tonal contrast. Ellsworth liked Robin, and he thought it bad form to paint Batman as a role model to the boy and young readers if he resorted to killing when convenient rather than using his great mind, incredible technology, and formidable training to find better solutions.
Less than a year after his debut, and only five months after he first started using a gun at all, Batman now had a rule against lethal force. The proto-Batman was fully crystalizing into the kind of character Finger felt Bruce Wayne was meant to be. In Batman #4, the Dark Knight openly acknowledges this rule to Robin. "Remember, we never kill with weapons of any kind!"