PN sequences over GF(q) are unsuitable directly for cryptography because of their strong linear structure. In the paper it is shown that in order to obtain the sequence with the same occurence of elements and with the same length as PN sequence, but having non-linear structure, it simply suffices to modulate the PN sequence by its cyclic shift using two-input quasigroup operator. Thus, such new sequences, named NLPN sequences, which means Non-Linear Pseudo-Noise sequences, can be easily generated over GF(q) for q ≥ 3. The method of generating the NLPN sequences is exhaustively explained by a detailed example concerning non-linear pseudo-noise sequences over GF(8). In the other example the way of constructing good keys generator for generalized stream-ciphers over the alphabet of order 256 is sketched. It is hoped that NLPN sequences will find many applications in such domains as cryptography,Monte-Carlo methods, spread-spectrum communication, GSM systems, random number generators, scrambling, testing VLSI chips and video encryption for pay-TV purposes.