We give a new construction of the moonshine module vertex operator algebra V ♮ over the real field, which was originally constructed in [FLM2]. The advantage of our construction is that we can easily prove the facts that V ♮ has a positive definite invariant bilinear form and Aut(V ♮) is the Monster simple group. In addition, we construct a lot of conformal vectors in V ♮ which give rise to 2A-...