  Using the Density Matrix Renormalization Group method, we determined the
phase diagram of a frustrated antiferromagnetic spin-$\frac 1 2$ ladder at zero
temperature. Two spin-gapped phases, the Haldane phase and the singlet phase,
are identified. A phase transition between the two phases occurs at any
non-zero value of frustration coupling $J_{\times}$. On the phase boundary, the
spin gap vanishes for sufficiently small $J_{\times}$. Crossing this non-gapped
line, the transition is of second order, while of first order for larger
$J_{\times}$. Striking frustration effects are predicted for ladder materials.
