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Type Ia Supernovae (SNe Ia) are widely used to measure distances in the Universe. Despite the recent progress achieved in SN Ia standardization, the Hubble diagram still shows some remaining intrinsic dispersion. The remaining scatter in supernova luminosity could be due to the environmental effects — progenitor age, chemical composition, surrounding dust, etc. In this study, we compared different tracers of the environment, i.d. the local and global colour (U − V), the local star formation rate, and the host stellar mass to the host galaxy morphology. We also studied the impact of SN galactocentric distance (376 Pantheon SNe Ia) and host-galaxy morphology (275 Pantheon SNe Ia) on the supernova light-curve parameters and the Hubble diagram. We confirmed that the stretch parameter depends on galactocentric distance and host morphology, but there is no significant correlation for the color. The supernovae with lower stretch value are hosted mainly by elliptical and lenticular galaxies or further from the center of host galaxies. The analysis of the Hubble diagram revealed that the mean distance modulus residual for SNe Ia in early-type galaxies is smaller than the one in late-type galaxies, which means that early-type galaxies contain brighter supernovae after stretch and colour corrections. Finally, we proposed the host-morphology step to account for the environmental effect and compared it with mass-step correction that is usually used in the modern cosmological analyses. In the epoch of large transient surveys such as the Vera Rubin Observatory’s Legacy Survey of Space and Time, a study of environment and other possible sources of systematic uncertainties in the cosmological analysis is of high priority.