  We propose a modified version of the quantum walk-based search algorithm
created by Shenvi, Kempe and Whaley, also known as the SKW algorithm. In our
version of the algorithm, we modified the evolution operator of the system so
that it is composed by the product of the shift operator associated to the
$2^n$-complete graph with self-loops and a perturbed coin operator based on the
Hadamard operator that works as an oracle for the search. The modified
evolution operator leads the opposite behavior as in the original algorithm,
that is, the probability to measure the target state is reduced. We call this
new behavior the $\textit{search complement}$. Taking a multigraph and matrix
approach, we were able to explain that the new algorithm decreases the
probability of the target state given that there are less paths that lead
towards the node that is associated to the target state in a Unitary Coined
Discrete-Time Quantum Walk. The search complement algorithm was executed
experimentally on IBM quantum processor $\textit{ibmq_manila}$ obtaining
statistical distances $\ell_1\leq 0.0895$ when decreasing the probability of
one state out of four.
