Based on properties of six special gauge-fixing terms of tetrad, some coordinate conditions are presented, which lead to that all second time derivative terms of tetrad in Einstein equation are removed when general relativity is expressed by tetrad formulation; this result does not contradict the well known fact that the number of propagating degrees of freedom in general relativity equals two. Under these coordinate conditions, we prove that general relativity becomes a fully singular Lagrange system in terms of the vierbein forms of the action and the Hamiltonian representation of the system...
