This paper discusses hadron energy reconstruction for the ATLAS barrel prototype combined calorimeter (consisting of a lead-liquid argon electromagnetic part and an iron-scintillator hadronic part) in the framework of the non-parametrical method. The non-parametrical method utilizes only the known e/ h ratios and the electron calibration constants and does not require the determination of any parameters by a minimization technique. Thus, this technique lends itself to an easy use in a first level trigger. The reconstructed mean values of the hadron energies are within ±1% of the true values and the fractional energy resolution is [(58±3)%/ E+(2.5±0.3)%]⊕(1.7±0.2)/E . The value of the e/ h ratio obtained for the electromagnetic compartment of the combined calorimeter is 1.74±0.04 and agrees with the prediction that e/ h>1.66 for this electromagnetic calorimeter. Results of a study of the longitudinal hadronic shower development are also presented. The data have been taken in the H8 beam line of the CERN SPS using pions of energies from 10 to 300 GeV.