Indeed. Research implicates a number of genes contributing to the illness. And, to make matters even more complicated, a set of genes can be related to a specific condition, but one person with those genes gets it, and another doesn't.
Eventually we may be able to determine risk of a person developing schizophrenia, just as we now can with breast and other cancers. But it seems highly unlikely that determination of schizophrenia (and a host of other conditions) will ever be reduced to a yes/no dichotomy as with Down’s Syndrome.