  A 2-dimensional braid over an oriented surface-knot $F$ is presented by a
graph called a chart on a surface diagram of $F$. We consider 2-dimensional
braids obtained by an addition of 1-handles equipped with chart loops. We
introduce moves of 1-handles with chart loops, called 1-handle moves, and we
investigate how much we can simplify a 2-dimensional braid by using 1-handle
moves. Further, we show that an addition of 1-handles with chart loops is an
unbraiding operation.
