A mechanism of origination of an even (in reference to the magnetic fi
eld) component of the Hall voltage in a spatially non-uniform supercon
ductor is discussed and its magnitude is estimated. The effect resulti
ng from the ''growth'' of a net of magnetic flux flow channels in a sa
mple under the increase of the transport current and/or of the magneti
c field manifests itself most vividly near T(c). The analogy with the
random walk problem permits one to deduce a distribution function of a
random quantity of the even Hall effect. The results obtained are in
accord with the experiments performed on spatially nonuniform high-tem
perature superconductors (YBCO-ceramics and YBCO-crystals).