  We present a traversable wormhole solution using the traceless $f(R,T)$
theory of gravity. In the $f(R,T)$ gravity, the Ricci scalar $R$ in the
Einstein-Hilbert action is replaced by a function of $R$ and trace of the
energy momentum tensor $T$. The traceless version of the $f(R,T)$ gravity gives
rise to a possible wormhole geometry without need for "exotic matter", which
violates the principle of causality. Using a physically plausible ansatz for
the wormhole's shape function, the traceless field equations lead to compliance
with the weak energy condition at very well defined intervals of the coupling
constant $\lambda$ in the $f(R,T)=R+2\lambda T$ form. Our solution leads to
other well-behaved energy conditions considering some possible values of the
parameter $\omega$ in the equation of state $p_r=\omega \rho$, with $p_r$ being
the radial pressure and $\rho $ the density. The energy conditions are obeyed
in the ranges $\lambda < -4\pi$ and $\omega > -1$. Through the calculation of
the Volume Integral Quantifier, one sees that this wormholes can be traversable
and respect the causality, since the amount of exotic matter in its interior
can be arbitrarily small.
