For it a program is writ, ten which does not contain loops and has the following properties. The program's original data are a normal algorithm A (its notation) and a word ~ , while the results are a Boolean value ~ and a word ~ . If A is applicable to word ~ , then we can indicate a finite memory such that the program, having worked on this memory, yields the value true as % and A(~) as ~. However, if A is not applicable to ~ , then the program does not work on any (finite) memory and always yields the value false as ~ . If the program works on an infinite memory, then after its work ~ takes the value true if and only if A is applicable to ~ ; moreover, in the case of applicability ~ takes the value A~) The present paper contains a more detailed exposition of the result published in Zap. Nauchn. Sem. Leningr. Otd. Mat. Inst. Akad. Nauk USSR, 70 (1977).