A quasi-isochoric scanning method has been used to study the phase diagram of helium from 200 to 460 K and from 70 to 240 kbar. The melting line is shown to be a smooth curve that lies close to extrapolations from much lower pressure. Also, no anomalies were observed near room temperature, and thus there is no evidence for an fcc-bcc transition in the solid phase. On the basis of the experiments, it is concluded that the fcc-bcc-fluid triple point reported by previous investigators does not exist. The implications for the phase diagram are discussed.