  We show that the Steinberg group $\text{St}(C_2,{\mathbb Z})$ associated with
the Lie type $C_2$ and with integer coefficients can be realized as a quotient
of the braid group $B_6$ by one relation. As an application we give a new
braid-like presentation of the symplectic modular group $\text{Sp}_4({\mathbb
Z})$.
