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We introduce a new impartial game, named Multiple Hook Removing Game (MHRGfor short). We also determine the $\mathcal{G}$-values of some game positions(including the starting positions) in MHRG$(m,n)$, the MHRG whose startingposition is the rectangular Young diagram of size $m\times n$ with the unimodalnumbering. In addition, we prove that MHRG$(m,n)$ is isomorphic, as games, toMHRG$(m,n+1)$ (if $m\le n$ and $m+n$ is even), and give a relationship betweenMHRG$(n,n+1)$ (and MHRG$(n,n)$) and HRG$(S_n)$, the Hook Removing Game in termsof shifted Young diagrams.

Multiple Hook Removing Game Whose Starting Position is a Rectangular Young Diagram with the Unimodal Numbering