Let A be a local ring which admits an exact pair x,y of zero divisors as
defined by Henriques and Sega. Assuming that this pair is regular and that
there exists a regular element on the A-module A/(x,y), we explicitly construct
an infinite family of non-isomorphic indecomposable totally reflexive
A-modules. In this setting, our construction provides an answer to a question
raised by Christensen, Piepmeyer, Striuli, and Takahashi. Furthermore, we
compute the module of homomorphisms between any two given modules from the
infinite family mentioned above.