  We investigate geometric aspects of the the B\"acklund transform of principal
contact element nets. A B\"acklund transform exists if and only if it the
principal contact element net is of constant negative Gaussian curvature (a
pseudosphere). We describe an elementary construction of the B\"acklund
transform and prove its correctness. Finally, we show that Bianchi's
Permutation Theorem remains valid in our discrete setting.
