Only if you where digging 6 feet down to bury the psalter.......

If there's a Holy Orthodox Monastery Near By ,Pay them a visit ...Tour the cemetery read the head stones find a place like a freshly bured grave that has mounds of dirt piled on it waiting to settle,use that, or bring a small garden shovel and find a area you like ,also you can plant a flower over the spot when burying the psalter....see how easy..
Hopefully your Talking about a Holy Orthodox Prayer Psalter and Not A roman Catholic One.....IF it's a Catholic Prayer Book Psalter Disregard Everything I said ...Just toss it in the garbage.......

Instead of burning you can bury it in hallow ground ,in a cemetery over a relative .....Church has a burial rite for
used worn out sacred books ,if im right.........
Thanks for the suggestion. I don't have this option though (family grave yard is 1000 miles away, they weren't Orthodox, and well, if you dig there you're going to dig someone up in all likelihood).