Bone marrow transplantation (BMT) patients are immunocompromised to a varying degree depending upon genetic relationship between donor and recipient with compromising therapy required for allogeneic transplants. Responses to influenza vaccine in this population have been poor and yet influenza virus infection can lead to serious disease. There is a need for prophylaxis against influenza in this population. One approach to improving immune responses to influenza vaccines in BMT patients could be to increase dosage and number of doses of vaccine. This approach has increased responses in a variety of populations. Moreover, using purified hemagglutinin (HA) vaccines in the form of rDNA-expressed HA protein in a baculovirus expression system has increased immune responses without an increase in reactogenicity. Researchers hypothesize that an increased dosage and 2 doses of a purified influenza vaccine will increase serum hemagglutination inhibition (HAI) and neutralizing antibody responses significantly over those following 2 doses of conventional vaccine in BMT patients. The primary objective of this study is to determine if 2 doses of a baculovirus-expressed recombinant trivalent influenza vaccine containing approximately 135 mcg per HA results in a significantly higher proportion of subjects achieving a Day 28 and Day 56 post vaccination increase in serum HAI and neutralizing antibody titer than seen after immunization with standard dose licensed trivalent inactivated influenza vaccine in immunosuppressed allogeneic HSCT (hematopoietic stem cell transplantation) recipients. The secondary objective is determination of the safety and tolerability of a two-dose regimen of recombinant, baculovirus-expressed HA containing approximately 135 mcg per HA administered by intramuscular injection to patients following allogeneic HSCT, and comparison of the geometric mean titers (GMT) of serum HAI and neutralizing antibody against all 3 virus strains contained in the vaccine. The study will enroll 100 adult (greater than or equal to 18 years of age) allogeneic HSCT recipients between 6 and 12 months following bone marrow transplantation, with no or stable chronic graft-versus-host disease, who are evaluated at the outpatient BMT clinic at M.D. Anderson Cancer Center. Subjects will be randomized to receive either licensed trivalent inactivated influenza vaccine (TIV) or baculovirus-expressed recombinant trivalent hemagglutinin vaccine (rHA0). All injections will be administered into the deltoid muscle. Subjects will be randomized (50 per group) to receive a vaccination on Day 0 and a second dose 4 weeks later. Subjects will be observed in the clinic for at least 20 minutes after inoculation, and subjects will maintain a memory aid to record oral temperature and solicited systemic and local adverse events (AE)s for 8 days (Day 0 through Day 7) after each immunization. Subjects will be seen on Day 2 and Day 30 (1-5 days after each vaccination) for an arm check, vital signs, assessment of possible AEs, concomitant medication assessment, and a targeted physical examination if indicated. Subjects will be contacted by phone on Day 8 and Day 36 (7-10 days after each vaccination) to review the memory aid and to assess for possible AEs or serious (S) AEs. Subjects will return to the clinic on Day 28 for AE and concomitant medication assessment, a targeted physical examination if indicated, and a review of the memory aid prior to receiving the second dose of vaccine. Serum for vaccine immunogenicity evaluations will be collected prior to vaccination at Days 0 and 28, and 56 days after the first vaccine dose. Participants will be involved in study related procedures for 6 months.