  We report the forbidden $6s^{2} ^{1}S_{0}\longrightarrow6s5d ^{3}D_{1}$
magnetic-dipole transition amplitude computed using multi-reference Fock-space
coupled-cluster theory. Our computed transition matrix element
($1.34\times10^{-4}\mu_{B}$) is in excellent agreement with the experimental
value ($1.33\times10^{-4}$ $\mu_{B}$). This value in combination with other
known quantities will be helpful to determine the parity non-conserving
amplitude for the $6s^{2} ^{1}S_{0}\longrightarrow6s5d ^{3}D_{1}$ transition in
atomic Yb. To our knowledge our calculation is the most accurate to date and
can be very important in the search of physics beyond the standard model. We
further report the $6s6p ^{3}P_{0}\longrightarrow6s6p ^{1}P_{1}$ and $6s5d
^{3}D_{1}\longrightarrow6s6p ^{3}P_{0}$ transition matrix elements which are
also in good agreement with the earlier theoretical estimates.
