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There is an apparent tension between cosmological parameters obtained from{\it Planck} cosmic microwave background radiation observations and thatderived from the observed magnitude-redshift relation for the type Ia supernova(SNe Ia). Here, we show that the tension can be alleviated, if we firstcalibrate, with the help of the distance-duality relation, the light-curvefitting parameters in the distance estimation in SNe Ia observations with theangular diameter distance data of the galaxy clusters and then re-estimate thedistances for the SNe Ia with the corrected fitting parameters. This was usedto explore their cosmological implications in the context of the spatially flatcosmology. We find a higher value for the matter density parameter, $\Omega_m$,as compared to that from the original SNLS3, which is in agreement with {\itPlanck} observations at $68.3\%$ confidence. Therefore, the tension between{\it Planck} measurements and SNe Ia observations regarding $\Omega_m$ can beeffectively alleviated without invoking new physics or resorting to extensionsfor the standard concordance model. Moreover, with the absolute magnitude of afiducial SNe Ia, $M$, determined first, we obtained a constraint on the Hubbleconstant with SNLS3 alone, which is also consistent with {\it Planck}.

A possible resolution of tension between {\it Planck} and Type Ia supernova observations