  The eavesdropping scheme proposed by W\'{o}jcik [Phys. Rev. Lett. {\bf
90},157901(2003)] on the quantum communication protocol of Bostr\"{o}m and
Felbinger [Phys. Rev. Lett. {\bf 89}, 187902(2002)] is improved by constituting
a new set of attack operations. The improved scheme only induces half of the
eavesdropping losses in W\'{o}jcik's scheme, therefore, in a larger domain of
the quantum channel transmission efficiency $\eta$, i.e., [0,75%], the
eavesdropper Eve can attack all the transmitted bits. Comparing to W\'{o}jcik's
scheme, in the improved scheme the eavesdropping (legitimate) information gain
does not vary in the $\eta$ domain of [0, 50%], while in the $\eta$ domain of
(50%, 75%] the less eavesdropping losses induce more eavesdropping information
gains, for Eve can attack {\it all} the transmitted bits and accordingly
eavesdropping information gains do {\it not} decrease. Moreover, for the
Bostr\"{o}m-Felbinger protocol, the insecurity upper bound of $\eta$ presented
by W\'{o}jcik is pushed up in the this paper, that is, according to
W\'{o}jcik's eavesdropping scheme, the Bostr\"{o}m-Felbinger protocol is not
secure for transmission efficiencies lower than almost 60%, while according to
the improved scheme, it is not secure for transmission efficiencies lower than
almost 80%.
