We have calculated the effects of an isotropic biquadratic exchange term having a coupling constant of moderate size [Formula: see text] upon the two-magnon bound state spectrum of an otherwise Heisenberg ferromagnet, with or without single-ion anisotropy, at zero temperature. The bound states are labelled by a wave vector q which we have taken to be in the [111] direction. The two principal results found are: (i) The large effect that K/J has in localizing the '"exchange coupled" bound state, S1 for all values of q above the two-magnon band, when it is sufficiently negative and the spin or pseudo-spin magnitude is of sufficient size. (ii) The change in the value of the wave vector, as K/J changes, at which the one-magnon spectrum crosses that of the "single-ion" bound state, S0.