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This paper proposes a new approximation algorithm $M$ for packing rectangles into a strip with unit width and unbounded height so as to minimize the total height of the packing. It is shown that for any list $L$ of rectangles, $M(L) \leq 2\cdot \mbox{OPT}(L)$, where $M(L)$ is the strip height actually used by the algorithm $M$ when applied to $L$ and OPT$(L)$ is the minimum possible height within which the rectangles in $L$ can be packed.