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A variant of the classical pseudo-arclength continuation method is proposed. Basically, the method can be viewed as pseudo-arclength continuation in (r, lambda) space where r is a functional of the solution. Another difference is a three-parameter predictor instead of the standard Euler step. This predictor, as well as the Newton corrector iteration, are justified and some numerical results for reaction-diffusion equations are presented. The method provides a simple algebraic check for symmetry breaking bifurcation, the most common type of secondary bifurcation in physical examples. Keywords: parameter dependent boundary value problems; continuation algorithm; singular points; symmetry breaking bifurcation; reaction diffusion equations.