We propose a revision of the system developed by Lepine+ (2007ApJ...669.1235L) for spectroscopic M-subdwarf classification. Based on an analysis of subdwarf spectra and templates from Savcheva+ (2014ApJ...794..145S), we show that the CaH1 feature originally proposed by Gizis (1997, J/AJ/113/806) is important in selecting reliable cool subdwarf spectra. This index should be used in combination with the [TiO5, CaH2+CaH3] relation provided by Lepine+ to avoid misclassification results. In the new system, the dwarf-subdwarf separators are first derived from a sample of more than 80000 M dwarfs and a "labeled" subdwarf subsample, and these objects are all visually identified from their optical spectra. Based on these two samples, we refit the initial [TiO5, CaH1] relation and propose a new [CaOH, CaH1] relation supplementing the [TiO5, CaH1] relation to reduce the impact of uncertainty in flux calibration on classification accuracy. In addition, we recalibrate the {zeta}TiO/CaH parameter defined in Lepine+ to enable its successful application to Large Sky Area Multi-Object Fiber Spectroscopic Telescope (LAMOST) spectra. Using this new system, we select candidates from LAMOST Data Release 4 and finally identify a set of 2791 new M-subdwarf stars, covering the spectral sequence from type M0 to M7. This sample contains a large number of objects located at low Galactic latitudes, especially in the Galactic anti-center direction, expanding beyond previously published halo- and thick disk-dominated samples. Besides, we detect magnetic activity in 141 objects. We present a catalog for this M-subdwarf sample, including radial velocities, spectral indices and errors, and activity flags, with a compilation of external data (photometric and Gaia Data Release 2 astrometric parameters).