  We investigate the explicit construction of the $WB_{2}$ algebra, which is
closed and associative for all values of the central charge $c$, using the
Jacobi identity and show the agreement with the results studied previously.
Then we illustrate a realization of $c=\frac{5}{2}$ free fermion model, which
is $m \rightarrow \infty$ limit of unitary minimal series, $c ( WB_{2}
)=\frac{5}{2} (1-\frac{12}{ (m+3)(m+4) })$ based on the cosets $( \hat{B_{2}}
\oplus \hat{B_{2}}, \hat{B_{2} })$ at level $(1,m).$ We confirm by explicit
computations that the bosonic currents in the $ WB_{2}$ algebra are indeed
given by the Casimir operators of $\hat{B_{2}}$ .
