Currently, the common method for determining the distances to galaxies for red giants (TRGB method) has a measurement limit of approximately 25~Mpc. In more distant galaxies, red giants are not visible in images of Hubble Space Telescope (HST). For such galaxies, we propose to use the already well-known method of the brightest stars, calibrated by us on the basis of HST telescope images for 150 galaxies of different types and luminosities. The obtained relationship between the luminosities of galaxies and their brightest stars can be used for irregular and spiral galaxies in a large span of their luminosities ranged from $M_B = -8^{\rm m}$ to $M_B = -19^{\rm m}$. Because the brightest stars have a luminosity 4--5 magnitudes higher than the luminosity of red giants, the method of the brightest stars can be applied for significantly more distant galaxies. The accuracy of the brightest blue star method is $0.\!^{\rm m}4$.