diff --git a/lib/matrix.rb b/lib/matrix.rb
index d452bf4..8455b88 100644
--- a/lib/matrix.rb
+++ b/lib/matrix.rb
@@ -661,22 +661,22 @@ class Matrix
   #++
 
   #
-  # Returns the determinant of the matrix.  If the matrix is not square, the
-  # result is 0. This method's algorithm is Gaussian elimination method
-  # and using Numeric#quo(). Beware that using Float values, with their
-  # usual lack of precision, can affect the value returned by this method.  Use
-  # Rational values or Matrix#det_e instead if this is important to you.
+  # Returns the determinant of the matrix.
+  # This method's algorithm is Bareiss algorithm, which has the nice properties
+  # of being exact for integers and minimizing the rounding error for floats.
   #
   #   Matrix[[7,6], [3,9]].determinant
-  #     => 45.0
+  #     => 45
   #
   def determinant
-    return 0 unless square?
+    Matrix.Raise ErrDimensionMismatch unless square?
 
     size = row_size
+    last = row_size - 1
     a = to_a
 
     det = 1
+    last_akk = 1
     size.times do |k|
       if (akk = a[k][k]) == 0
         i = (k+1 ... size).find {|ii|
@@ -685,16 +685,16 @@ class Matrix
         return 0 if i.nil?
         a[i], a[k] = a[k], a[i]
         akk = a[k][k]
-        det *= -1
+        det = -det
       end
 
-      (k + 1 ... size).each do |ii|
-        q = a[ii][k].quo(akk)
-        (k + 1 ... size).each do |j|
-          a[ii][j] -= a[k][j] * q
+      (k+1).upto(last) do |ii|
+        last.downto(k) do |j|
+          a[ii][j] =  (akk * a[ii][j] - a[ii][k] * a[k][j]) / last_akk
         end
       end
-      det *= akk
+      det = det / last_akk * akk
+      last_akk = akk
     end
     det
   end