The aim of this study is to assess the long-term safety of C1-esterase inhibitor (C1-INH) in preventing hereditary angioedema (HAE) attacks when it is administered under the skin of subjects with HAE. The safety of participating subjects will be assessed for up to 54 weeks. The long-term efficacy of C1-INH will also be assessed. Each eligible subject will enter the treatment phase, wherein subjects will be randomized to treatment with either low- or medium-volume C1-INH. Subjects who have an insufficient treatment response during the study will be given an opportunity to undergo a dose increase. The study aims to enroll eligible subjects who completed study CSL830_3001 (NCT01912456). Subjects who did not participate in study CSL830_3001 may also participate, if eligible and if space permits. Subjects from the United States (US) who complete Treatment Period 2 will be allowed to participate in an Extension Period. During the Extension Period participating US subjects will continue to receive treatment with open-label CSL830 for up to an additional 88 weeks.