We describe a new direct digital synthesizer (DDS) in which output tuning resolution is flexibly controlled. The new DDS has an extended phase accumulator (EPA) controlled by two frequency control words; one determines the wave number within a single EPA operation cycle, and the other determines the length of the cycle. The EPA allows the DDS to provide jitter-free signals, the frequencies of which are given by arbitrary fractional expressions. (The denominator is fixed in conventional DDS that use normal phase accumulators.) Experimental results showed that the EPA worked well, allowing flexible output tuning resolution.