  We have identified a first group of 33 new candidates for symbiotic stars
(SySt) of the accreting-only variety among the 600,255 stars so far observed by
the GALAH high-resolution spectroscopic survey of the Southern Hemisphere, more
than doubling the number of those previously known. GALAH aims to high
latitudes and this offers the possibility to sound the Galaxy for new SySt away
from the usual Plane and Bulge hunting regions. In this paper we focus on SySt
of the M spectral type, showing an Halpha emission with a peak in excess of 0.5
above the adjacent continuum level, and not affected by coherent radial
pulsations. These constraints will be relaxed in future studies. The 33 new
candidate SySt were subjected to a vast array of follow-up confirmatory
observations (X-ray/UV observations with the Swift satellite, search for
optical flickering, presence of a near-UV upturn in ground-based photometric
and spectroscopic data, radial velocity changes suggestive of orbital motion,
variability of the emission line profiles). According to Gaia eDR3 parallaxes,
the new SySt are located at the tip of the Giant Branch, sharing the same
distribution in M(Ks) of the well established SySt. The accretion luminosities
of the new SySt are in the range 1-10 Lsun, corresponding to mass-accretion
rates of 0.1-1x10(-9) Msun/yr for WDs of 1 Msun. The M giant of one of the new
SySt presents a large Lithium over-abundance.
