  To determine the equation of state of the universe, we propose to use a new
independent variable $R\equiv (H_0/c)(d_L(z)/(1+z))$, where $H_0$ and $d_L(z)$
are the present Hubble parameter and the luminosity distance, respectively. For
the flat universe suggested from the observation of the anisotropy of cosmic
microwave background, the density and the pressure are expressed as
$\rho/\rho_0=4(df/dR)^2/f^6$ and $p/\rho_0=-4/3(d^2f/dR^2)/f^5$ where $\rho_0$
is the present density and $f(R)=1/\sqrt{1+z(R)}$. In $(R, f)$ plane the sign
as well as the strength of the pressure is in proportion to the curvature of
the curve $f(R)$. We propose to adopt a Pade-like expression of
$f(R)=1/\sqrt{u}$ with $u\equiv 1+\sum\limits_{n=1}^{N}u_nR^n$. For flat
$\Lambda$ model the expansion up to N=7 has at most an error $< 0.2%$ for $z <
1.7$ and any value of $\Lambda$. We also propose a general method to determine
the equation of state of the universe which has $N-1$ free parameters. If the
number of parameters are smaller than $N-1$, there is a consistency check of
the equation of state so that we may confirm or refute each model.
