diff --git a/NEWS.md b/NEWS.md
index a1a5e445..c0696fd1 100755
--- a/NEWS.md
+++ b/NEWS.md
@@ -7,6 +7,7 @@ Fix: regression of the `stars` package makes `rasterize_terrain()` extremely slo
 New: `catalog_intersects()` support a `SpatExtent`
 Fix: `lidR` can fully works without `raster` ans `sp`
 Fix: [#742](https://github.com/r-lidar/lidR/discussions/742)
+Fix: local maximum filter `lmf()` with a fixed windows is now 20 times faster.
 
 ## lidR v4.1.0 (Release date: 2024-01-31)
 
diff --git a/src/LAS.cpp b/src/LAS.cpp
index 4dbd6b8f..cca57515 100644
--- a/src/LAS.cpp
+++ b/src/LAS.cpp
@@ -358,12 +358,20 @@ NumericVector LAS::compute_range(DataFrame flightlines)
 
 void LAS::filter_local_maxima(NumericVector ws, double min_height, bool circular)
 {
+  char UKN = 0;
+  char NLM = 1;
+  char LMX = 2;
+
   bool abort = false;
   bool vws = ws.length() > 1;
 
   SpatialIndex tree(las);
   Progress pb(npoints, "Local maximum filter: ");
 
+  std::vector<char> state(npoints);
+  std::fill(state.begin(), state.end(), 0);
+  for (int i = 0 ; i < npoints ; i++) { if (Z[i] < min_height) state[i] = NLM; }
+
   #pragma omp parallel for num_threads(ncpu)
   for (unsigned int i = 0 ; i < npoints ; i++)
   {
@@ -373,8 +381,7 @@ void LAS::filter_local_maxima(NumericVector ws, double min_height, bool circular
 
     double hws = (vws) ? ws[i]/2 : ws[0]/2;
 
-    if (Z[i] < min_height)
-      continue;
+    if (state[i] == NLM) continue;
 
     // Get the points within a windows centered on the current point
     std::vector<PointXYZ> pts;
@@ -403,7 +410,13 @@ void LAS::filter_local_maxima(NumericVector ws, double min_height, bool circular
       if(z > zmax)
       {
         is_lm = false;
-        break;
+      }
+
+      // If the windows size is fixed, then, if a point is below the central point
+      // we are sure it is not a LM
+      if (!vws && z < Z[i])
+      {
+        state[pt.id] = NLM;
       }
 
       // Found one equal. If this one was already tagged LM we can't have two lm
@@ -456,6 +469,10 @@ void LAS::filter_local_maxima(NumericVector ws)
   else
     Rcpp::stop("C++ unexpected internal error in 'filter_local_maxima': invalid windows."); // # nocov
 
+  std::vector<char> state(npoints);
+  std::fill(state.begin(), state.end(), 0);
+  for (int i = 0 ; i < npoints ; i++) { if (Z[i] < min_height) state[i] = NLM; }
+
   SpatialIndex tree(las, skip);
   Progress pb(npoints, "Local maximum filter: ");