Can the signature of quadratic form be negative?

Question

I have a canonical form of the quadratic form. The canonical form is $y_1^2-y_2^2-y_3^2$.

So, the rank will be 3, and the the index will be 1. So, by the formula for signature,

signature = 2s-r = 2(1) - 3 = -1

I wanted to know if this is possible, can the signature of a quadratic form be negative?