Erasure coding has been extensively deployed in today's data centers to tackle prevalent failures, yet it is prone to substantial cross-rack traffic for parity updates. In this paper, we propose a new rack-coordinated update mechanism to suppress the cross-rack update traffic, which comprises two successive phases: a delta-collecting phase that collects data delta chunks, and another selective parity update phase that renews the parity chunks based on the update pattern and parity layout. We further design <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math>${\sf RackCU}$</tex-math></inline-formula> , an optimal rack-coordinated update solution that achieves the theoretical lower bound of the cross-rack update traffic. We also perform reliability analysis, demonstrating that <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math>${\sf RackCU}$</tex-math></inline-formula> can attain a lower data loss probability via shortening the update procedure. We conduct extensive evaluations, in terms of large-scale simulation and real-world data center experiments. We show that <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math>${\sf RackCU}$</tex-math></inline-formula> can reduce 16.5-77.1% of the cross-rack update traffic and hence improve 24.9-772.0% of the update throughput.