  A new type of resistive plate chamber with thin-film electrodes based on
diamond-like carbon is under development for background identification in the
MEG II experiment. Installed in a low-momentum and high-intensity muon beam,
the detector is required to have extremely low mass and a high rate capability.
A single-layer prototype detector with 2 cm $\times$ 2 cm size was constructed
and evaluated to have a high rate capability of 1 MHz/cm$^2$ low-momentum
muons. For a higher rate capability and scalability of the detector size, the
electrodes to supply high voltage were segmented at a 1 cm pitch by
implementing a conductive pattern on diamond-like carbon. Using the new
electrodes, a four-layer prototype detector was constructed and evaluated to
have a 46% detection efficiency with only a single layer active at a rate of
$\cal O$(10 kHz). The result with the new electrodes is promising to achieve
the required detection efficiency of 90% at a rate of 4 MHz/cm$^2$ with all the
layers active.
