Do you have another staircase going to the second floor in front of or behind this staircase?
Ron

No, the other stairs are located on the other side of the basement and lead into the garage. Actually that staircase is in the garage rather than being in the basement and don't take up any space in the basement. In the 80s someone added onto the house and added the garage stairs. The kitchen stairs however are inside the basement and are original to the house. It's just one story...a small 60s style bungalow type. Mlou

As long as the ceiling rafters above the staircase are not cut or are spliced above the wall being removed you should be okay. You really need to know that this wall is only a partition wall. Filling the floor area once you remove the staircase is pretty easy. Put joists, the same size as you have in the floor now, every 16". Hang joist hangers on each joist and use the proper nails and nailing pattern called for on the joist hanger. Plywood up to the existing level and you should be ready to get on with the rest of the renovation.
Ron

Ron, thanks so much. Mlou