Specific problems arising in the use of the method of renormalization group and ε expansion in the theory of developed turbulence are discussed: the necessity to take into account the dependence of the model parameters on the expansion parameter ε and the large magnitude of the physical value of the expansion parameter. It is shown that quantities independent of the amplitude of the correlation function of the random force possess a uniquely defined ε expansion. On the example of the two-loop calculation of the Kolmogorov constant and the turbulent Prandtl number, effectiveness of the improved expansion is demonstrated, which uses an approximate summation of the high-order terms of the ε expansion.