  We first present a new Lagrangian of general relativity, which can be divided
into kinetic energy term and potential energy term. Taking advantage of
vierbein formalism, we reduce the kinetic energy term to a sum of five positive
terms and one negative term. Some gauge conditions removing the negative
kinetic energy term are discussed. Finally, we present a Lagrangian that only
include positive kinetic energy terms. To remove the negative kinetic energy
term leads to a new field equation of general relativity in which there are at
least five equations of constraint and at most five dynamical equations, this
characteristic is different from the normal Einstein field equation in which
there are four equations of constraint and six dynamical equations.
