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Let $C_n$ be the group of conjugating automorphisms. Valerij G. Bardakovdefined a representation $\rho$ of $C_n$, which is an extension ofLawrence-Krammer representation of the braid group $B_n$. Bardakov proved thatthe representation $\rho$ is unfaithful for $n \geq 5$. The cases $n=3,4$remain open. M. N. Nasser and M. N. Abdulrahim made attempts towards thefaithfulness of $\rho$ in the case $n=3$. In this work, we prove that $\rho$ isunfaithful in the both cases $n=3$ and $n=4$.

The faithfulness of an extension of Lawrence-Krammer representation on the group of conjugating automorphisms $C_n$ in the cases $n=3$ and $n=4$