Strongly prime rings may be defined as prime rings with simple central closure. This paper is concerned with further investigation of such rings. Various characterizations, particularly in terms of symmetric zero divisors, are given. We prove that the central closure of a strongly (semi-)prime ring may be obtained by a certain symmetric perfect one sided localization. Complements of strongly prime ideals are described in terms of strongly multiplicative sets of rings. Moreover, some relations between a ring and its multiplication ring are examined.