Summary: T. Kohonen and P. Somervuo have shown that self organizing maps (SOMs) are not restricted to numerical data. This paper proposes a symbolic measure that is used to implement a string self organizing map based on SOM algorithm. Such measure between two strings is a new string. Computation over strings is performed using a priority relationship among symbols, in this case, symbolic measure is able to generate new symbols. A complementary operation is defined in order to apply such measure to DNA strands. Finally, an algorithm is proposed in order to be able to implement a string self organizing map. This paper discusses the possibility of defining neural networks to rely on similarity instead of distance and shows examples of such networks for symbol strings.