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Abstract
A new continuous strictly increasing singular function is described with the help of the ternary and binary systems for real number representation; in this, our function is similar to Cantor's function, but in other aspects it is quite unusual. We are able to determine a condition to identify many points for which the derivative vanishes or is infinite; for other singular functions constructed with the help of a system of representation of real numbers, this condition depends on some metrical properties of the growth of averages of the sum of all the digits of the representation, but in the case of this new function, it depends on the frequency of occurrence of the digit 2 in the usual ternary expansion of a number.
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