  The branching fractions from the excited state $6P_{1/2}$ of singly charged
barium ion has been measured with a precision $0.05%$ in an ion trap
experiment. This measurement along with the known value of the upper state
life-time allowed the determination of the dipole matrix elements for the
transitions $P-S$ and $P-D$ to below one percent level. Therefore, for the
first time it is now possible to compare the many body calculations of these
matrix elements at level which is of significance to any parity
non-conservation experiment on barium ion. Moreover, these dipole matrix
elements are the most significant contributors to the parity violating matrix
element between the $S-D$ transition, contributing upto $90%$ to the total. Our
results on the dipole matrix elements are $3.306\pm0.014$ and $3.036\pm0.016$
for the $S-P$ and $P-D$ transitions respectively.
