The search towards the fundamental natural units of mass, distance and time began with Weyl [1,2], Eddington [3] and Dirac [4]. Max Planck derived fundamental units purely from fundamental physical constants h, c and G [5]. Weinberg proposed a formula for obtaining a unit of mass using the constants: h , c , G and H0 , where H0 is Hubble’s constant [6]. Tank showed [7] that Planck’s unit of length is a geometric-mean of two un-equal lengths; namely Compton-wavelength and Gravitational-radius of every particle, so the units, obtained by taking square-root of a set of fundamental physical constants, may not be truly fundamental units. Weinberg obtained a unit of mass by taking cube-root of a set of fundamental-constants, so we are not sure whether the multiplication of three masses in Weinberg’s formula are of the same masses or of different masses. Therefore, here we shall derive a unit of mass without taking any square-root or cube-root. There is a possibility of physical existence of a particle with this mass, h H0 / c^2; and it seems that a photon decays into a lighter photon plus this new particle of mass : h H0 / c^2 .