Operators ( ₁＋₂＋ 3＋₄,₁－₂,₁－₃ and ₁－₄) satisfy the commutation relation [₁＋₂＋ 3＋₄,₁－₂]＝0,[ ₁＋₂＋ 3＋₄,₁－₂]＝0,and [₁－₃,₁－₄〖WTB Z 〗].Therefore,they have common eigenvectors.By two particles entang led state representation inspired,we first construct a pure Gaussian integral.Then we split the integrated operator into a pure state projection operator.Finaly,the eigenvector of four c ompatible operators [₁＋₂＋ ₃＋₄,₁－₂,₁－₃ and ₁－₄) is proposed in Fock space by the technique of integration within an ordered product of operators(IWOP).It s complete and orthogonal characteristics are analyzed.Its entanglement is discussed by obtaining Schmidt decomposition in momentum representation and in coordinate representation.The results show that it makes up a new quantum mechanical representation and is an entangled state.On the other ha nd,we also calculate the asymmetric ket-bra integral.Then we construct a new four-mode s queezed operator by using this entangled state representation and discuss its squeezed property .Further more,a four-mode squeezed vacuum state is constructed.The fluctuations of its two quadrature components are calculated.The results show that it has a squeezing effect.