Do Not Increase - DNI

Instructions on a good-till-cancelled buy-limit or stop order that tell a broker not to increase the number of shares bought or sold in the event of a stock dividend or stock split.

Investopedia Says:
This is telling a broker not to increase the shares of your order when the number of shares you own increases.

Abbreviated DNI. Instruction on good-till-cancelled buy limit and sell stop orders that prevent the quantity from changing in the event of a stock Split or stock dividend.