The cure: Keep your elbows close to your body and swing your arms mostly back and foward, as if reaching for your wallet from a back pocket on the backstroke.
As they come forward, your hands should not cross the center line and should come up no further than your breasts.
This arm motion will give power to your walk. Your feet generally move only as fast as your arms.
This motion lets you concentrate on power from your rear leg without wasting motion in front of your body. It also looks far less silly.
Photo used by permission of Ero-fit (c) 2000