Lightening Dyed Black Hair?

I dyed my hair black and it is growing out and I am wanting to know if there is a way that I can dye my hair a lighter color and not get orange. The color I used was a mix of the darkest black and the darkest blue mixed together. I am naturally a dirty blonde and would like to get back to that or even lighter is fine. Any ideas on the best way to go about changing from black to another color without getting an orange or red color?