A K-dependent adiabatic approach is suggested to study the Renner-Teller effect in triatomic molecules using a two-dimensional Hilbert space approximation in the electronic degree of freedom. The theory is developed in hyperspherical coordinates, and approximately includes the electronic spin-orbit interaction. The adiabatic Hamiltonians are expressed in terms of a K-dependent effective potential energy surface. Eigenpairs are calculated by solving the time-independent Schrodinger equation, which is represented in a mixed grid/basis set. The method is applied to the (A) over tilde <--(X) over tilde band system of bromomethylene (H/DCBr). The results obtained show that the Renner-Teller effect in this molecule is pronounced, particularly in the excited (A) over tilde (1)A" state. The results are compared to recent experimental measurements and good agreement is found.