The invention relates to a turbine blade (1), a turbine shaft (2) having such a turbine blade (1), a turbine system comprising a turbine shaft (2) having such a turbine blade (1), and a method for installing the turbine blade (1), resulting in that the turbine blade (1) is made of a fiber composite material and, at the same time, the bearing strength of the turbine blade (1) or the blade root (3) of the turbine blade (1) is increased relative to metal turbine blades by reducing stress concentrations at locations of the blade root (3) at which the blade root (3) is supported by corresponding wall segments (6) of a groove (4) of the turbine shaft (2), thus extending the service life of the turbine blade (1) and thus the turbine shaft (2) and the turbine system having such turbine blades (1). The aim is achieved by a particularly fine fit of the blade root (3) of the turbine blade (1) in the shape of the groove (4) of the turbine shaft (2), due to the effect of heating on the blade root (3) brought about by precautionary heating (8) during assembly to the turbine shaft (2), and consequently of auto-adaptation of the shape to the shape of the groove (4) of the turbine shaft (2).