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Type Ia supernovae (SNe) are excellent distance indicators in the Universe. Observations of distant SNe Ia led to the discovery of the accelerating expansion of the Universe. The most recent analysis of SNe Ia indicates that considering a flat $\Lambda$CDM cosmology, the contribution of dark energy in the total density of the Universe is $\sim$ 70\%. Cosmological parameters are estimated from the ``luminosity distance-redshift'' relation of SNe~using the Hubble diagrams. Currently a lot of attention is paid to standardization of SNe, i.e. to increase of the accuracy of luminosity distance determination. The uncertainty on the redshift is quite often considered negligible. The redshift used in ``luminosity distance-redshift'' relation is a cosmological redshift, i.e. the redshift due to the expansion of the Universe. In fact the redshift observed on the Earth also includes the contribution from the Doppler effect induced by peculiar velocities related to the Hubble flow. It is well known that peculiar velocity of SNe~introduces an additional uncertainty to the Hubble diagram and therefore have an impact on the estimation of cosmological parameters. To minimize the influence of poorly constrained peculiar velocities, in cosmological analyses a standard value of 300-400 km s$^{-1}$ peculiar velocity dispersion is added in quadrature to the redshift uncertainty. It has nonetheless been observed that velocity dispersion can exceed 1000 km s$^{-1}$~in galaxy clusters and therefore, the dispersion inside the cluster can be greater than the one usually assumed in cosmological analyses and can affect the distance measurements. To take this effect into account we study SNe~Ia that are exploded in the galaxy clusters. Using 145 SNe~Ia from the Nearby Supernova Factory we found 20 objects that belong to the clusters. We used the galaxy cluster redshift instead the host galaxy redshift to construct the Hubble diagram. The applied technique allowed to improve the distance measurements for low and intermediate redshifts and to decrease the spread on the Hubble diagram. The $wRMS$ is improved from 0.150~mag to 0.149~mag with 1.7-$\sigma$ significance. We also found that the dispersion on the Hubble diagram of 20 SNe~Ia in galaxy clusters is smaller than the one of SNe outside the clusters. It could be due to the fact that supernovae in clusters are more standard and therefore more suitable for the distance measurements. The main outcome of this work is the confirmation that the correction for the peculiar velocities of the galaxies inside the clusters is important for distance measurements and has to be taken into account in future cosmological surveys (such as LSST).