A new proof of the Mahler conjecture in R2 is given. In order to prove the result, we
introduce a new method the vertex removal method; i.e., for any origin-symmetric
polygon P, there exists a linear image P contained in the unit disk B2, and there exist
three contiguous vertices of P lying on the boundary of B2. We can show that the volume product
of P decreases when we remove the middle vertex of the three vertices.