  Estimating the source parameters of gravitational waves from compact binary
coalescence(CBC) is a key analysis task in gravitational-wave astronomy. To
deal with the increasing detection rate of CBC signals, optimizing the
parameter estimation analysis is crucial. The analysis typically employs a
stochastic sampling technique such as Markov Chain Monte Carlo(MCMC), where the
source parameter space is explored and regions of high Bayesian posterior
probability density are found. One of the bottlenecks slowing down the analysis
is the non-trivial correlation between masses and spins of colliding objects,
which makes the exploration of mass$\unicode{x2013}$spin space extremely
inefficient. We introduce a new set of mass$\unicode{x2013}$spin sampling
parameters which makes the posterior distribution to be simple in the new
parameter space, regardless of the true values of the parameters. The new
parameter combinations are obtained as the principal components of the Fisher
matrix for the restricted 1.5 post-Newtonian waveform. Our re-parameterization
improves the efficiency of MCMC by a factor of $\sim10$ for binary neutron star
with narrow-spin prior ($|\vec{\chi}|<0.05$) and $\sim100$ with broad-spin
prior ($|\vec{\chi}|<0.99$), under the assumption that the binary has spins
aligned with its orbital angular momentum.
