It is possible to dye brown hair black without bleaching it.
When you want to dye your hair darker, it is not necessary to use bleach. The only time bleach is needed for coloring is if your desired result is a lighter color than you naturally are, or if you have dyed your hair a dark color in the past. Going from a natural or even dyed brown to a shiny black color can therefore be achieved without the use of bleach.
Tips for dyeing your hair black
You need to make sure you use the right color to cover brown hair effectively, especially if you want to achieve a true black color.
If your hair is naturally warm and you want a cool shade, be sure to use a color with cool or ashy undertones to remove the heat. Using the wrong color can lead to a muddy color versus a beautiful shiny black.