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We present a spectral analysis of the binary G 224-58 AB that consists of thecoolest M extreme subdwarf (esdM5.5) and a brighter primary (esdK5). Thisbinary may serve as a benchmark for metallicity measurement calibrations and asa test-bed for atmospheric and evolutionary models for esdM objects.  We determine abundances primarily using high resolution optical spectra ofthe primary. Other parameters were determined from the fits of syntheticspectra computed with these abundances to the observed spectra from 0.4 to 2.5microns for both components.  We determine \Tef =4625 $\pm$ 100 K, \logg = 4.5 $\pm$ 0.5 for the Acomponent and \Tef = 3200 $\pm$ 100 K, \logg = 5.0 $\pm$ 0.5, for the Bcomponent. We obtained abundances of [Mg/H]=$-$1.51$\pm$0.08,[Ca/H]=$-$1.39$\pm$0.03, [Ti/H]=$-$1.37$\pm$0.03 for alpha group elements and[CrH]=$-$1.88$\pm$0.07, [Mn/H]=$-$1.96$\pm$0.06, [Fe/H]=$-$1.92$\pm$0.02,[Ni/H]=$-$1.81$\pm$0.05 and [Ba/H]W=$-$1.87$\pm$0.11 for iron group elementsfrom fits to the spectral lines observed in the optical and infrared spectralregions of the primary. We find consistent abundances with fits to thesecondary albeit at lower signal-to-noise.  Abundances of elements in \ga and \gb atmospheres cannot be described by onemetallicity parameter. The offset of $\sim$ 0.4 dex between the abundancesderived from alpha element and iron group elements corresponds with ourexpectation for metal-deficient stars. We thus clarify that some indices usedto date to measure metallicities for establishing esdM stars based on CaH, MgHand TiO band system strength ratios in the optical and H$_2$O in the infraredrelate to abundances of alpha-element group rather than to iron peak elements.For metal deficient M dwarfs with [Fe/H] < -1.0, this provides a readyexplanation for apparently inconsistent "metallicities" derived using differentmethods.

Probing M subdwarf metallicity with an esdK5+esdM5.5 binary