In the fission yeast Schizosaccharomyces pombe, interphase microtubules (MTs) position the nucleus [1, 2], which in turn positions the cell-division plane [1, 3]. It is unclear how the spindle orients, with respect to the predetermined division plane, to ensure that the chromosomes are segregated across this plane. It has been proposed that, during prometaphase, the astral MT interaction with the cell cortex aligns the spindle with the cell axis [4] and also participates in a spindle orientation checkpoint (SOC), which delays entry into anaphase as long as the spindle is misaligned [5-7]. Here, we trace the position of the spindle throughout mitosis in a single-cell assay. We find no evidence for the SOC. We show that the spindle is remarkably well aligned with the cell longitudinal axis at the onset of mitosis, by growing along the axis of the adjacent interphase MT. Misalignment of nascent spindles can give rise to anucleate cells when spindle elongation is impaired. We propose a new role for interphase microtubules: through interaction with the spindle pole body, interphase microtubules determine the initial alignment of the spindle in the subsequent cell division.