Database design question

I have a table on a bought-in application with about 350,000 rows. It has a column defined as an index, but in fact the column contains contains nothing for any row. Therefore every one of the 350,000 rows has the same index value, which is clearly undesireable. However, what the design is clearly meant to achieve is fast selection of a single row when the column has a non-null value. Any hints or tips for this? Thanks Neil Truby Chase Bank Bournemouth, UK