So you are saying the national deficit went down because Clinton had a surplus? It actually went up nearly $18b

Democratic Senator Ernest Hollings, said on October 28, 1999:

So the table itself, according to the figures issued yesterday, showed the Federal Government ran a surplus. Absolutely false. This reporter ought to do his work. This crowd never has asked for or kept up with or checked the facts. Eric Planin--all he has to do is not spread rumors or get into the political message. Both Democrats and Republicans are all running this year and next and saying surplus, surplus. Look what we have done. It is false.

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If have $10 left in your checking account at the end of the month but you took another thousand out of your savings account and spend that too, you have a $990 deficit, not a $10 surplus. Simple math.

There may have been $236 b left over after on budget spending the year Bush took office but there was also off budget spending that was taken out of the intra governmental holdings which resulted in a near $18b increase in the national deficit.

If there is a surplus, if the government spends less than it takes in, the deficit goes up not down. Simple math.

Calculating the national debt

The annual change in debt is not equal to the "total deficit" typically reported in the media. Social Security payroll taxes and benefit payments, along with the net balance of the U.S. Postal Service are considered "off-budget" while most other expenditure and receipt categories are considered "on-budget." The total federal deficit is the sum of the on-budget deficit (or surplus) and the off-budget deficit (or surplus). Since FY1960, the federal government has run on-budget deficits except for FY1999 and FY2000, and total federal deficits except in FY1969 and FY1998-FY2001.
In large part because of Social Security surpluses, the total deficit is smaller than the on-budget deficit. The surplus of Social Security payroll taxes over benefit payments is spent by the government for other purposes. However, the government credits the Social Security Trust fund for the surplus amount, adding to the "intragovernmental debt." The total federal debt is divided into "intragovernmental debt" and "debt held by the public." In other words, spending the "off budget" Social Security surplus adds to the total national debt (by increasing the intragovernmental debt) while the surplus reduces the "total" deficit reported in the media.
Certain spending called "supplemental appropriations" is outside the budget process entirely but adds to the national debt. Funding for the Iraq and Afghanistan wars was accounted for this way prior to the Obama administration. Certain stimulus measures and earmarks are also outside the budget process.
For example, in FY2008 an off-budget surplus of $183 billion reduced the on-budget deficit of $642 billion, resulting in a total federal deficit of $459 billion. Media often reported the latter figure. The national debt increased by $1,017 billion between the end of FY2007 and the end of FY2008. The federal government publishes the total debt owed (public and intra governmental holdings) at the end of each fiscal year and since FY1957, the amount of debt held by the federal government has increased each year.

Simple Math.