  The equation of motion for comohogeneity-one Nambu-Goto strings in flat space
$\mathbb{R}^{n,1}$ has been investigated. We first classify possible forms of
the Killing vector fields in $\mathbb{R}^{n,1}$ after appropriate action of the
Poincar\'e group. Then, all possible forms of the Hamiltonian for the
cohomogeneity-one Nambu-Goto strings are determined. It has been shown that the
system always has the maximum number of functionally independent, pair-wise
commuting conserved quantities, i.e. it is completely integrable. We have also
determined all the possible coordinate forms of the Killing vector basis for
the 2-dimensional non-commutative Lie algebra.
