  Precision measurements of the Sunyaev Zeldovich (SZ) effect in upcoming blank
sky surveys require theoretical understanding of all physical processes with
$\ga 10%$ effects on the SZ power spectrum. We show that, observed cluster
magnetic field could reduce the SZ power spectrum by $\sim 20%$ at $l\sim
4000$, where the SZ power spectrum will be precisely measured by the Sunyaev
Zeldovich array (SZA) and the Atacama cosmology telescope (ACT). At smaller
scale, this effect is larger and could reach a factor of several. Such effect
must be considered for an unbiased interpretation of the SZ data. Though the
magnetic effect on the SZ power spectrum is very similar to that of radiative
cooling, it is measurable by multi-band CMB polarization measurement.
