  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 $\sim0.03$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+-2.28(random)+-5.06(systematic)
km/s/Mpc and H_0 = 74.37+-2.27(random)+-4.92(systematic) km/s/Mpc,
respectively. Hubble constants calculated using the Galactic PL relations are
also briefly discussed and presented in the last section of this Letter.
