  We show that the previously known off-shell nilpotent (s_{(a)b}^2 = 0) and
absolutely anticommuting (s_b s_{ab} + s_{ab} s_b = 0)
Becchi-Rouet-Stora-Tyutin (BRST) transformations (s_b) and anti-BRST
transformations (s_{ab}) are the symmetry transformations of the appropriate
Lagrangian densities of a four (3 + 1)-dimensional (4D) free Abelian 2-form
gauge theory which do not explicitly incorporate a very specific constrained
field condition through a Lagrange multiplier 4D vector field. The above
condition, which is the analogue of the Curci-Ferrari restriction of the
non-Abelian 1-form gauge theory, emerges from the Euler-Lagrange equations of
motion of our present theory and ensures the absolute anticommutativity of the
transformations s_{(a)b}. Thus, the coupled Lagrangian densities, proposed in
our present investigation, are aesthetically more appealing and more
economical.
