Just take $R^4=C^2$ with  complex 
coordinates $z_1=x_1+ i y_1, z_2= x_2 + i y_2$ and the flat  
metric $-dz_1 d\bar z_1 + dz_2 d \bar z_2$. It has signature (2,2). As the group of isometries  take the group of  $x_1 $-translations, it preserves the canonic symplectic form $dx_1\wedge dy_1 + dx_2 \wedge dy_2$, and actually is generated by the function $y_1$. The symplectic reduction gives you a positively definite metric $dz^2d\bar z_2$.