  As one of the major components of the interstellar medium, the ionized gas in
our Milky Way, especially the low-density diffuse component, has not been
extensively observed in the radio band. The Galactic Plane Pulsar Snapshot
(GPPS) survey covers the sky area within the Galactic latitude of $\pm10^\circ$
around the Galactic plane visible by the Five-hundred-meter Aperture Spherical
radio Telescope (FAST), and the spectral line data are simultaneously recorded
during the pulsar survey observations. With an integration time of 5 minutes
for each beam, the GPPS survey project provides the most sensitive piggyback
spectra for tens of radio recombination lines (RRLs) in the band of 1000$-$1500
MHz for H$n\alpha$, He$n\alpha$, C$n\alpha$, as well as H$n\beta$ and
H$n\gamma$. We processed the spectral data of RRLs, and obtained a sensitive
averaged H$n\alpha$ RRL map of a sky area of 88 square degrees in the inner
Galaxy of 33$^\circ$ $\leqslant l \leqslant$ 55$^\circ$ and $|b| \leqslant$
2.0$^\circ$. The final spectral data of the H$n\alpha$ RRLs have a spatial
resolution of $\sim$3$^\prime$, a spectral resolution of 2.2 km s$^{-1}$, and a
typical spectral rms noise of 0.25 mJy beam$^{-1}$ or 6.3 mK in main-beam
brightness temperature. The new H$n\alpha$ RRL map shows complex structural
features dominated by a number of HII regions and large extended diffuse
ionized gas regions. We detect about 94% of the known HII regions and confirm
43 WISE HII regions in the observed sky area. Several large HII regions or
star-forming complexes in the distant outer Galaxy are resolved in the map of
H$n\alpha$ RRLs. Extended RRL features of the diffuse ionized gas are detected.
The RRL data products of the GPPS survey will be published and updated at
http://zmtt.bao.ac.cn/MilkyWayFAST/
