The bisection method for polynomial real root isolation was introduced by Collins and Akritas in 1976. In 1981 Mignotte introduced the polynomials Aa,n(x)=xn−2(ax−1)2, a an integer, a≥2 and n≥3. First we prove that if a is odd then the computing time of the bisection method when applied to Aa,n dominates where d is the maximum norm of Aa,n. Then we prove that if A is any polynomial of degree n with maximum norm d then the computing time of the bisection method, with a minor improvement regarding homothetic transformations, is dominated by . It follows that the maximum computing time of the bisection method is codominant with .