  In this paper we present the proof of the convergence of the critical bond
percolation exploration process on the square lattice to the trace of
SLE$_{6}$. This is an important conjecture in mathematical physics and
probability. The case of critical site percolation on the hexagonal lattice was
established in the seminal work of Smirnov via proving Cardy's formula. Our
proof uses a series of transformations and conditioning to construct a pair of
paths: the $+\partial$CBP and the $-\partial$CBP. The convergence in the site
percolation case on the hexagonal lattice allows us to obtain certain estimates
on the scaling limit of the $+\partial$CBP and the $-\partial$CBP. By
considering a path which is the concatenation of $+\partial$CBPs and
$-\partial$CBPs in an alternating manner, we can prove the convergence in the
case of bond percolation on the square lattice.
