  We show that a modular unit on two copies of the upper half-plane is a
Borcherds product if and only if its boundary divisor is a special boundary
divisor. Therefore, we define a subspace of the space of invariant vectors for
the Weil representation which maps surjectively onto the space of modular units
that are Borcherds products. Moreover, we show that every boundary divisor of a
Borcherds product can be obtained in this way. As a byproduct we obtain new
identities of eta products.
