It is well-known that the peak brightness of the Type Ia supernovae calibrated with Cepheid distances can be used to determine the Hubble constant .
The Cepheid distances to host galaxies of the calibrating supernovae are usually obtained using the period-luminosity ( PL ) relation derived from Large Magellanic Cloud ( LMC ) Cepheids .
However recent empirical studies provide evidence that the LMC PL relation is not linear .
In this Letter we determine the Hubble constant using both the linear and non-linear LMC Cepheid PL relations as calibrating relations to four galaxies that hosted Type Ia supernovae .
Our results suggest that the obtained values of the Hubble constant are similar .
However a typical error of \sim 0.03 mag .
has to be added ( in quadrature ) to the systematic error for the Hubble constant when the linear LMC PL relation is used , assuming that the LMC PL relation is indeed non-linear .
This is important in minimizing the total error of the Hubble constant in the era of precision cosmology .
The Hubble constants calibrated from the linear and non-linear LMC PL relation are H _ { 0 } = 74.92 \pm 2.28 \mathrm { ( random ) } \pm 5.06 \mathrm { ( systematic ) } \mathrm { km } % \mathrm { s } ^ { -1 } \mathrm { Mpc } ^ { -1 } and H _ { 0 } = 74.37 \pm 2.27 \mathrm { ( random ) } \pm 4.92 \mathrm { ( systematic ) } \mathrm { km } % \mathrm { s } ^ { -1 } \mathrm { Mpc } ^ { -1 } , respectively .
Hubble constants calculated using the Galactic PL relations are also briefly discussed and presented in the last section of this Letter .