Accurate chromosome segregation requires a cohesin-mediated physical attachment between chromosomes that are to be segregated apart, and a bipolar spindle with microtubule plus ends emanating from exactly two poles toward the paired chromosomes. We asked whether the striking bipolar structure of C. elegans meiotic chromosomes is required for bipolarity of acentriolar female meiotic spindles by time-lapse imaging of mutants that lack cohesion between chromosomes. Both a spo-11 rec-8 coh-4 coh-3 quadruple mutant and a spo-11 rec-8 double mutant entered M phase with separated sister chromatids lacking any cohesion. However, the quadruple mutant formed an apolar spindle whereas the double mutant formed a bipolar spindle that segregated chromatids into two roughly equal masses. Residual non-cohesive COH-3/4-dependent cohesin on separated sister chromatids of the double mutant was sufficient to recruit haspin-dependent Aurora B kinase, which mediated bipolar spindle assembly in the apparent absence of chromosomal bipolarity. We hypothesized that cohesin-dependent Aurora B might activate or inhibit spindle assembly factors in a manner that would affect their localization on chromosomes and found that the chromosomal localization patterns of KLP-7 and CLS-2 correlated with Aurora B loading on chromosomes. These results demonstrate that cohesin is essential for spindle assembly and chromosome segregation independent of its role in sister chromatid cohesion.