Published data for large amplitude asymptotic giant branch variables in the Large Magellanic Cloud are re-analysed to establish the constants for an infrared ( K ) period-luminosity relation of the form : M _ { K } = \rho [ \log P - 2.38 ] + \delta .
A slope of \rho = -3.51 \pm 0.20 and a zero point of \delta = -7.15 \pm 0.06 are found for oxygen-rich Miras ( if a distance modulus of 18.39 \pm 0.05 is used for the LMC ) .
Assuming this slope is applicable to Galactic Miras we discuss the zero-point for these stars using the revised Hipparcos parallaxes together with published VLBI parallaxes for OH Masers and Miras in Globular Clusters .
These result in a mean zero-point of \delta = -7.25 \pm 0.07 for O-rich Galactic Miras .
The zero-point for Miras in the Galactic Bulge is not significantly different from this value .

Carbon-rich stars are also discussed and provide results that are consistent with the above numbers , but with higher uncertainties .
Within the uncertainties there is no evidence for a significant difference between the period-luminosity relation zero-points for systems with different metallicity .