We use a new phase-calibration strategy to calibrate the phase of 86 GHz VLBI observations of the FR I radio galaxy NGC 4261. Instead of switching between a calibrator source and the target source, the target was observed while rapidly switching between the target frequency and a lower reference frequency. Self-calibration at the reference frequency yielded phase corrections which were multiplied with the frequency ratio and applied to the target frequency visibilities. The resulting detection of NGC 4261 is, to our knowledge, the first of NGC 4261 with 86 GHz VLBI, and it is also the weakest source so far detected with VLBI at that frequency.