r^2 r'^2}$ would represent a membrane intersecting on a string localized within both fivebranes. More generally, one could take $H_T = 1+ {Q_T^{(1)} \over r^2} + {Q_T^{(2)}
 \over r'^2}+ {Q_T^{(3)} \over r^2 r'^2}$. In the remaining of this article we shall, for simplicity, use $H_T=H_F^{(1)} H_F^{(2)}$. The near-horizon limit of (A) has geometry $adS_3 \xx S^3 \xx S^3 \xx E^2$ and preserves $1/2$ of supersymmetry as we will show in the next section. So there is supersymmetry doubling also in this case.

Now consider intersection (A) with harmonic functions $H_F^{(1)}=1+{Q_1\over r'^2}$, $H_F^{(2)}=1+{Q_2\over r^2}$ and $H_T=H_F^{(1)} H_F^{(2)}$ where $r^2=x_3^2+x_4^2+x_5^2+x_6^2$ and $r'^2=x_7^2+x_8^2+x_9^2+x_{10}^2$. We can consider various limits of this solution. First, if we go very far from one of the fivebranes, $r\rightarrow\infty$ ($r'\rightarrow\infty$), we recover the standard intersection (a), i.e. $M2\perp M5$[^10]. If we go near the horizon in the latter intersection, $r'\rightarrow0$ ($r\rightarrow 0$), we find again the near-horizon geometry $adS_3 \xx E^5 \xx S^3$. We describe in detail the interpolating structure of solution (A) in figure 2.

(11,7)(0,0) (0,0)[(4,1)[$(adS_3 \xx E^2 \xx S^3 \xx S^3)_{1/2}$]{}]{} (3,1) (3,1)[(0,1)[5.1]{}]{} (3,1)[(1,0)[4.9]{}]{} (8,0.5)[(3,1)[$(adS_3 \xx E^5 \xx S^3)_{1/2}$]{}]{} (1,5.8)[(3,1)[$(adS_3 \xx E^5 \xx S^3)_{1/2}$]{}]{} (5,3)[(1,1)[$({\rm A})_{1/4}$]{}]{} (6,3.5)[(1,0)[1.9]{}]{} (5.5,4)[(0,1)[2]{}]{} (5.9,3.9)[(1,1)[2]{}]{} (5,5.8)[(1,1)[$(\rm a)_{1/4}$]{}]{} (8,3)[(1,1)[$(\rm a)_{1/4}$]{}]{} (8,5.8)[(1,1)[$({\cal M}^{11})_1$]{}]{} (6,.5)[$r$]{} 