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Systematic investigations of experimental partial photoneutron cross sections for many medium and heavy nuclei show that many of them do not satisfy specially introduced criteria of data reliability. That was found out that in various energy ranges of initial photons the ratios F1 = SIG(G,1n)/SIG(G,xn) = SIG(G,1n)/SIG[(G,1n) + 2(G,2n) + 3(G,3n) + …] have physically forbidden negative values and at the same time corresponding ratios F2 = SIG(G,2n)/SIG(G,xn) have physically unreliable values larger 0.50. That means that experimental neutron multiplicity sorting has been done erroneously because of large systematic uncertainties. New data free of such kind uncertainties were evaluated for 91,94Zr using new experimentally-theoretical method. The only experimental reaction cross section SIGexp(G,xn) used was shared into partial parts using the equations Ftheori = SIGtheor(G,1n)/SIGtheor(G,xn) of combined pre–equilibrium exciton model of photonuclear reactions. The way of new cross sections evaluation – SIGeval(G,in) = Ftheori • SIGexp(G,xn) – means that competition between partial reactions is in accordance with model free from neutron multiplicity sorting problems and their sum SIGeval(G,xn) is equal to SIGexp(G,xn) also free from problems mentioned. New cross sections were evaluated for (G,n) and (G,2n) reactions in the case of 91Zr and for (G,n), (G,2n) and (G,3n) in the case of 94Zr. Using evaluated partial reactions cross sections for both isotopes new data were obtained for total photoneutron reaction SIG[(G,1n) + (G,2n) + (G,3n) + …] ~ SIG(G,abs). Large deviations of evaluated cross sections from experimental ones are discussed in details.