If the Office you have was "bundled" with the old computer, and not a
separately purchased retail copy, then the answer is yes. The license
for that version, known as OEM (original equipment manufacturer), is
inexpensive to the vendor, but it's allowed only on the original
hardware.
If it was separately purchased, then you can move it to the new
computer if you completely uninstall it from the old computer. You may
have to use telephone activation (if it's Office XP or 2003) if the
software complains that it can't activate.
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