  An unknotting operation is a local change on knot diagrams. Any knot diagram
can be transformed into a trivial unknot diagram by a series of unknotting
operations plus some Reidemeister moves. Unknotting operations have significant
importance in knot theory; they are used to study the complexity of knots and
invariants of knots. Unknotting operations are also important in biology,
chemistry, and physics to study the sophisticated entanglements of strings,
organic compounds, and DNA. In this paper, we introduced a new unknotting
operation called the diagonal move for classical and welded knots. We show that
the crossing change, Delta-move, Sharp-move, Gamma-move, n-gon move, pass move,
and 4-move can be realized by a sequence of diagonal moves. We also define the
distance induced by the diagonal move and study its properties.
