Large amount of sediment?

Hi. I have brewed up only my 2nd brew but it seem to have a large amount of sediment in the bottles, to the point of not really drinkable. (currently the brew has been bottled for 4 weeks) I was thinking of emptying each bottle into a large container via I filter then re-bottling, should I leave it in the container to go flat then re-carbonate and would this work? Or would I be better of to just re-bottle right after it's been filtered?

If you dump your beer out you run the risk of oxydizing the beer. Rather than do that chill the beer down for a couple of weeks which will compact the sediment, and pout carefully. And for your next batch figure out what your doing wrong. I get almost no sediment in my bottles simply by opting for a month long primary and rackign carefully to my bottling bucket. Just enough to carbonate the beer.

after bottle conditioning, refrigeration works wonders
My first brew I had a difficult time siphoning and bottling due to lack of experience with the equipment.. it got all mixed up and I had all sorts of floaties and generally "dirty" beer. In fact, I was ready to dump it and start over but then I remembered something my dad once (actually several times) told me. "Son, quit being such a GodD***ed P***y." -- So, I pressed on, went ahead and bottled all of it.. aged it for two weeks I think, then let it ride in the fridge.. I've still got 3x16oz bottles of it, and over time, it has settled and with a careful pour, and minimal shaking beforehand: Excellence.

I've learned with Homebrewing that patience is paramount.