Context : We present a spectral analysis of the binary G 224-58 AB that consists of the coolest M extreme subdwarf ( esdM5.5 ) and a brighter primary ( esdK5 ) .
This binary may serve as a benchmark for metallicity measurement calibrations and as a test-bed for atmospheric and evolutionary models for esdM objects .

Aims : We perform the analysis of optical and infrared spectra of both components to determine their parameters .

Methods : We determine abundances primarily using high resolution optical spectra of the primary .
Other parameters were determined from the fits of synthetic spectra computed with these abundances to the observed spectra from 0.4 to 2.5 microns for both components .

Results : We determine T _ { eff } =4625 \pm 100 K , \log~ { } g = 4.5 \pm 0.5 for the A component and T _ { eff } = 3200 \pm 100 K , \log~ { } g = 5.0 \pm 0.5 , for the B component .
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 ] = - 1.87 \pm 0.11 for iron group elements from fits to the spectral lines observed in the optical and infrared spectral regions of the primary .
We find consistent abundances with fits to the secondary albeit at lower signal-to-noise .

Conclusions : Abundances of different elements in G 224-58 A and G 224-58 B atmospheres can not be described by one metallicity parameter .
The offset of \sim 0.4 dex between the abundances derived from alpha element and iron group elements corresponds with our expectation for metal-deficient stars .
We thus clarify that some indices used to date to measure metallicities for establishing esdM stars based on CaH , MgH and TiO band system strength ratios in the optical and H _ { 2 } O in the infrared relate 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 ready explanation for apparently inconsistent ” metallicities ” derived using different methods .