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

On addition of 1-handles with chart loops to 2-dimensional braids