Let $X$ be a complex Hilbert space ($\dim X $ is at least three) and $A$ a bounded selfadjoint operator on $X$ ($\dim AX $ is neither 1 nor 2). In this paper we study a continuous functional $h$ on $X$ which is approximately quadratic on $A$-orthogonal vectors (i.e., $(\alpha_1)$ is satisfied provided that $(Ax,y)=0$). We find that there exists a unique continuous functional $h_1$ (given by ($\alpha_2$)) which is quadratic on $A$-orthogonal vectors (i.e., $(\alpha_3)$ holds) and which is near $h$ (i.e., $(\alpha_4)$ holds).